This video covers essential matrix operations including finding the order of AB^T (where A is x×p and B is q×r, resulting in x×q when p=r), identifying skew symmetric matrices (where A^T = -A), understanding singular matrices (determinant = 0) versus non-singular matrices (determinant ≠ 0), and calculating matrix trace (sum of diagonal elements). The instructor emphasizes efficient exam strategies, including using calculator shortcuts for matrix operations and time management techniques for mathematics examinations.
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Deep Dive
BLENDO EXAM SUCCESS is liveAdded:
like a friend's There's a Oh, there's a you don't settle.
You don't set up no login. I do the other one first. Then I will just collect person food.
Wonder this time. I've already sent it.
How are you?
Good morning class.
So let's quickly walk through this uh mathematics so that uh you can go home and do your final revision at home. The revision you do at home is the most important Okay. The first question that we have today is on matrix on matrix.
Let's A and B The matrices.
The two matrices. The two matrices.
The two matrices.
AB transpose is defined.
Find the order of AB transpose.
Find the order of AB transpose.
All right. So what you do is this when you are told that abt where t is transpose okay a remains x by p this x by p is the order q by r order. So when we have a transpose of order you now notice that let's say that a x p then transpose of a x will be what p x p * what x so what is the transpose of b if b is q by r transpose will be what arrow by Now a B transpose meaning that if you multiply this A by this A it is possible it is defined. So because it is defined we can now find the order of the resulting uh solution. So here we already have what? X by P. when you multiply it by R by Q. Okay. The condition for this if it is possible if it is defined the condition for this to hold is P must be equal to what? R. They say find the order. Find the what? Order. They did not ask you to find the condition when P is equal to what? R. Find the order. So here the condition for this thing to be defined is P is equal to what? R.
Then the order will be what? X by what?
Q.
X by Q. So the answer to this question is what? X by Q.
The answer is X by Q.
Don't you have a Microsoft Word? This thing is not showing all the value where Microsoft is not showing everything. Some things are cutting.
Some things are cutting.
Mhm.
This everything is showing here.
So we need to be very fast. I hope this one is understood.
>> This one is introduction.
I just want you to remind yourself. We have done this one before, right? Uhhuh.
So Let's Hey, this means what?
A T is equal to A I J then is called what?
A is called what?
A is called what?
Huh?
You can't see. Can you see now?
>> You know the answer. Ba. When you see it like this, you know the answer, right?
Uhhuh.
Okay. What is the answer?
What is the answer?
Eh my friend, you are looking for the answer.
Next question. Right.
Don't cry.
You are what? Talk to me. Huh? No. You say something now.
I should what? talk to Lord Jesus.
>> Okay, I should write the answer. What's the answer?
The answer is a skew what symmetric matrix when it is what?
Negative.
What does it mean? The transpose of a matrix that is excuse me symmetric matrix the transpose of a matrix that gives that matrix. If a is a matrix and you transpose a it gives back the negative of that matrix it becomes what symmetry. Have you seen that a matrix a is a i right? Then a transpose is also a i what? J. But negative of it. Remember what a transpose is. When you transpose a i j what will you see? J I ab. But you are still seeing what? I J. But what negative with negative that is skill symmetric.
Now can I clean the board now since you have seen the answer?
>> Be fast please.
No.
By this time you're not supposed to be confused over these things. I dropped this thing earlier when you start asking me question on what I have dropped before. You know that you never came.
If your telegram is having problem, sort it out immediately.
>> What was the answer?
I love this 3 by what? Simple.
>> Who's 3x2?
>> Are you saying 3x3?
Uh, hope you not go back to your note and check it.
When you see these two matrix, okay, pay attention please. When you see these two matrices, determine the order of AB or transpose. It resembles that other one AB. That one is AB transpose. This one is what? AB or transpose.
They are not the same.
Hey, naturally somebody will say let us multiply. Ab 3 * 4, four * 3, 5 * this. You go again.
Three * this. No, 3 * is a row by column. 3 * 4 2 * 5 + 4 * 3 * this, 2 * this, 3 * this. Like that. You start wasting your time. You multiply row by column. You see how I just remembered it? Row by column. You don't need to cram it. When you are trying to do it and uh you are not getting it. Remember if you want to multiply is row by what? Column.
Multiply row. Show this is row. Multiply by what? Column. Your answer will come out immediately. If you multiply three by four, what will you get?
>> Huh?
>> You write 12. Let me show you something.
You multiply two by five. What will you get?
>> You say plus what?
>> 10. Do you understand? Because you are still maintaining the first row and the first what? Column. You add it.
That shows that it is first row. First what? Column.
Then you come again. Yes. Is what? First row ab is what? Second column. Abby. You now say 3 * 3 is what? H. Will I write it here?
First row say I will still maintain first row. Second column I will come to second column along first row. Have you seen it now? So with the multiplication of this you will know. But the good news is that you are not dealing with this in your exam. But just have it in mind that if you say 3 * 3 you have what? 9. First row second column. First row second column. 2 * 1 is what? two. I will now say plus what? Two. Because all the multiplication was done in where? First row. Second column. Do you understand?
Then first row again I will come here because it's still what? First row.
Which column now? Uhhuh. So 3 * -2 will give me what? Minus 6. 2 * 4 will give me what? I will now say plus what?
Eight. Because I am still on first row.
Third what? Columns. First row. Third column. I will stop because I don't have any other thing to multiply again.
I will continue like that if I wish by saying four * 4.
Which row is this now?
>> Good. Second row. What? So four * 4 is what? Can I write 16 here? 1 * 5 is what I will write plus what five because I am where now second row what first column do you understand I will come back again second row second column second row second column anything I multiply I will add it 4 * 3 is what I will write 12 I will add Again 1 * 1 is what? 1 12 + 1. Second row. Second column. Then the next one is what?
Second row. What? Third column. I will have what? 4 * -2 is what? - 8 and plus what? Four. I am done with second row. I am done with what? Second row. I go to the next row which is what? Third row.
Third row is five and minus one. Do you understand?
5 * 4 you give me what >> I will write 20 I am still in third row first column right >> -1 * 5 give me what - 5 have you seen it because minus * is what minus third row still on third row second column 5 * 3 is What?
Huh?
>> I'll write 15.
-1 * 1 is what? - one. Third row. Third column.
5 * -2 is what? - 10. -1 * 4 is what?
Minus what?
Naturally, this is beautiful.
I have succeeded in wasting my whole time. And now this is what you are supposed to do. Why you are writing your CBT if you don't know what I want to show you now? Do you understand? And you end up wasting your time. That is why those cramming past question I pity you because tomorrow will shock you. People ask a crime pass question and it shocked them. So you don't even need to cram who will you be who if you don't write you blame anybody. You will not blame anybody. You blame yourself.
So in this case this is this will give us our answer. Should I tell you the answer now from here? The question says determine the order of AB transpose AB and we start moving this one to the column. So first row we take you come to first. So 12 + 10 is what?
Uhhuh. Let's get it. 22. Uhhuh.
Uhhuh. Here is what?
Uhhuh.
Uhhuh.
Here is what is what is what?
>> Good. I want you to see how to transpose this thing. Now is AB alone. It's not ABt. But what? AB. Now I want to get AB.
This is what a human being will do that that knows how to solve matrix that is very good expert nobody sent all this your method you are using but if you know it and you are showing another person I'm not follow this person can solve but it's just so useless now a transpose is equal to what 22 112 we come to the first column right 112. Next one is what? 21 13 - 4. Next one is what? 15 14. This is the answer to the question. They say what is the order of AB transpose. Now what is the order of AB transpose?
One 1 2 3 1 2 3. Have you seen it now?
>> Row is three and column is what? Three.
You now say the answer is what? 3 by 3.
This is the only thing they want you to get not all this nonsense.
Then how will you get it without doing this? That is why we are here. Watch this is the question. Now let's put it as shortcut.
Here is what is what? Talk to me now. A is what?
>> We are about to get this using shortcut.
A alone is what?
>> Say it again.
>> Again.
>> Three by what?
Do how do we know the one that is row and the one that is column? Remember it is row by column. Right? How many rows do we have?
>> H.
>> How many columns? That is three by what?
Two. Do you understand? Now three rows and what? Two columns. Now coming to B.
B is what?
B is how many rows is in B?
>> H.
Good. Good. Now watch this.
I'll write two by what? Three.
automatically looking at AB they didn't say AB all transpose is defined I'll be one to know whether it is defined or not that is where I will now use my shortcut but here you need to solve it until you get something if it is not defined you cannot even proceed in solving it is defined that is why we are able to solve and we got an answer. So because it is defined but how will I know that it is defined? I gave you one rule before right in that first as I started for it to be defined what happens 2 must be equal to what? Two is 2 = 2.
>> Yes.
>> If this two now we say 2 is equal to two that is the condition for it to be defined. Now it is defined. What is the order of the resulting solution?
3x 3 bar. This is order of what? A is it order of a transpose? No. If AB is 3x3, take note order of a square matrix is that square matrix. Is that clear? For example, order of 2x2.
If you now find a transpose of it, okay, transpose of a square matrix is that matrix.
Like if you have 2x2 or what is the transpose of 2x2? 2x2. So when you have AB to give us 3x3, what is the transpose of AB?
>> 3x3. So automatically a b transpose is equal to what 3x3. So how will you solve it? When you look for the transpose here and here the order here and here. Okay.
You multiply by getting the condition 2 two. Okay. If two and three here it will not work. But if three and two is here it should not work. It must be equal 3 three or 22. Is that clear? Immediately you notice that here is 22. The last numbers becomes the order becomes the what as we have seen that it is the order transpose of this order will still give us three by what? Three. So 3x3 is the answer. Okay. I don't want you to waste your time using this method. Use this method. Is this me not short?
Would you like to use this one? Uhhuh.
So unless you are writing a theory exam freely use this one. Are you writing theory?
you're writing CBT. So this is what you use. Okay?
Don't don't don't ever prove yourself that you are very good in mathematics to any idiot because that person will mock you. Know that who this what is this one doing now? A whole lecturer can even mock you. You are serving. You have failed. That's what we tell you. If any lecturer sees you serving serving, he said this don't know what he's doing.
They will want you to look at the question and get it easily with the shortest time.
Now, next question.
The question has been.
>> All right.
Next question, please. No time.
What is a singular matrix?
Let A be a member of why I'm writing out this symbol.
These are not the things you have to cram.
If you cram it, you may have problem.
You need to know what you are doing.
Let A be a member of capital M.
M is order of what?
N by N. This N by N means what? Square matrix. Say square matrix.
>> Square matrix. In the exam they may not put a is a member. This thing the bit that is a square matrix. So what they will say is if A is a square matrix do you understand? If A is a square matrix.
Uhhuh.
A. Therefore the condition for square matrix is this. You see something like this a is equal to a i j. Are you getting it now? Such that I is equal to what? J. This same means that it is a square matrix. It is what? A square matrix.
This thing and this thing they are the same. A is member of A is a square matrix. This is it. Then the continuation you start having other condition but the first condition you be given is this where I is what row J is what column I is equal to J row is equal to what column N is what row N is what column when it say N by N it means what row by what column meaning that row is equal to what column but our Question is a is called non-s singular. If what happen?
Huh?
Sure. I said it before. B see what you will see in the hall this night. I'm going to I like that telegram where where you are free to post everything.
You will be stressing yourself using another phone to be snapping rubbish because the thing will now be dim.
Now determinant a determinant a this means determinant a if a is non-s singular determinant a is not equal to what >> zero if a is called a singular matrix.
Determinant A is equal to what?
>> Z. Do you understand?
Okay, understand though.
I should say it again.
We have almost 100 questions to tackle.
Okay, say it again. Take time.
Now, which one do you want me to say again?
Is it a non-s singular or singular?
Both. A non-s singular matrix is a matrix whose determinant is not equal to what? Zero. Why? A singular matrix is a matrix whose determinant is equal to what?
>> Zero. I down is clear. What of a singleton uh a singleton?
A singleton is what? A matrix that has only one word. No single thing is used in set right not in matrix one is insert is insert. Okay.
Singleton in set singular a matrix. Is that clear? A matrix is set to be singular when the determinant is zero.
Then singleton a singleton set is a set to be a set is set to be singleton when it has only one what element.
What of an empty set? Is this thing an empty set?
>> Is this one an empty set?
>> Is this one An empty set.
>> No.
>> Is this one an empty set?
>> No.
>> An empty set.
>> If a dot is inside is not an empty what? Set. So if this symbol is inside is not an empty what?
Set. Take note of it because of uh those that can easily forget.
Now the answer of this one is clear, right?
It is better to be clear than you cram what you don't know.
I know of people that cram what they don't know. They went to the hall, they saw the question but could not remember the answer.
Now if x and y are real root if x and y are real leave this root are real comma Express 2 - 3 I 4 + 2 I.
What's the answer? Can I calculate or solve it? Chap.
Anyone that can solve don't waste time or should I start solving it or is there anybody that is aspiring not to have calculator tomorrow?
2 * 4 is what?
2 * 4 is what?
Eight. Abby. 2 * 2 is what? Some people are waiting for me to point and I square is equal to what?
Minus one here will be plus right?
>> So 6 + 8 is what?
Uh 6 + 8 is what? 40 is it 40?
14.
>> Yes.
>> Or you have 4 - 12 is what?
>> Is that what you got?
>> 14 - 8 I right. Very correct.
Very correct.
Can I is now?
Huh?
If X and Y compute 2 - I - 3 + 2 I 5 - 4 I. You know what to do, right?
You're already in complex mode. Do it fast.
Point calculator. Press mode.
Press mode two.
Shift. Shift. Shift.
Is it showing?
Is it showing?
Are you sure?
Orientation does what?
I hear your phone. Do you have that?
Go to the Go to YouTube.
and share it.
Go to YouTube.
>> Yeah. Go to YouTube.
>> Let me know. Go to check whe >> is it clear?
>> Do you don't have that?
Open to your YouTube.
What's the answer?
>> 8 + what?
>> 55 I right?
Very correct.
Have you done that?
>> Now who has phone that is are you online? Where's your phone? Go online.
Go to YouTube.
You have data first. Yeah.
I want to check check whether it's clear.
It's not open. Open it now.
Open blend exam sources.
>> Exam success.
Then the answer.
>> It's not clear.
>> He's back.
But >> no, not there's something to You cannot go and I'm using my phone. I'll share it on Telegram. Show it on this phone. Okay.
All right.
No. Listen, please.
Huh?
All your complex number.
You notice that they they're very simple, right? Any complex number they will give to you is the same thing. So pray your own is complex number. If X and Y array express 2 - 3 3 - 2 I in the form of X + Y I. Oh yeah. What is the answer?
Express this in this form.
Put it in calculator first.
Put in calculator so that we can go to the next question.
Have you done that?
What was this?
For this one, the answer is minus 5 / 2 - 1 /2. Is that what you got?
>> For this one, the answer is I just want you to be confirming the way you are using calculator to get your answer.
11 / 17. Abby minus what? 10 / 17. So that if you not get it, you correct yourself. How many of you saw the one I posted this morning?
Have you solved all of them? Hh in telegram.
So don't worry until I remove it. That's you know can remove it.
Those first question that is flying up and down.
Let it continue to fly.
If you finish allowing you to fly in your head in the night, you fly back to Telegram because if you like confuse yourself, I will do my own when you listen. You'll be very happy.
I've told you this.
Express 3 + 4 I 2 + I over 1 - I >> Let me set this down.
This is very dark.
It's kind Sorry, I said I disturb you.
>> All right.
Have you solved this one?
>> What did you get?
Please, what did they say? You got for this question. Abby, >> let me see.
is a mistake. But let's see if uh you see this question, pay attention. I'll still send it in the group. But listen, if you see it like this, show your answer is what? Say it again.
>> No problem. This is correct. Okay. But if you see the same question, you point you see this one in your calculator.
You do not see it in the option. Huh?
>> Locate this one is a mistake.
But write this one.
This one. Put aesthetics.
This is the question.
This is the error answer. Tick the error answer.
You will not see this one in the option.
Instead of leaving it blank, you take this error answer.
In case they correct it, you pick this one.
I just have to write down so that you see it clearly.
Ah.
What was the last thing I said about matrix?
It was It's not It's just counting. I have other things to say about it.
Hey is equal to today is the day I have to say everything. If I don't say everything, there will be no other day to say it.
Determine the trace of a matrix.
Determine the trace of a >> H.
Right?
>> Very correct.
Trace >> is equal to 10. Do you know how >> trace is 10? Trace is what?
>> Trace is 10.
Summation of the diagonal of what? A matrix is the trace. Just add the diagonal.
Before I write this one, I hope you know the answer.
Look at it here.
A x B 3 then H.
Find X A Y B.
A is equal to B + C.
Do you remember the answer?
>> 7 what?
>> 7433. Say it again.
>> Uh 7 4 33. You are just adding B to C, right? 3 + 4 2 + 2 2 + 1 >> 4 - 1 answer 7. Simple. Now you're not supposed to stress yourself.
Should I write the answer?
>> 7 x = 7.
A is equal to what? Four. Y is 3. And this is what? 3. That is 7433.
7433.
7433.
I hope you are with your calculator. Now this one needs calculator but if it is asked just know the answer direct.
>> Can you see? Do you have your phone data? Go online and be saying it if you cannot see.
It's clear.
She is clear. Oh my. She doesn't want to see. Let me Are you on it? Are you on?
>> Yeah. Take your phone.
>> All right.
Next question.
You know how to solve it with calculator, right?
First you want to keep the answer.
Solve it with calculator.
Solve it calculator. What will you get?
When you punch everything, the answer is what? Zero.
Confirm it with the calculator. When I give you answer, I confirm.
>> Do you know how to solve it? Calculator.
>> Can you press mode?
I have passed. Give me a calculator.
Press mode.
>> Huh?
Press mode.
Have you pressed mode?
>> Follow my instruction.
Press six.
Have you pressed six?
>> Press one.
Then finally what is this? Say two by two.
>> What is this?
>> So this how you have forgotten it tomorrow. Thank god you are here.
Install identity what? Which is one zero and what one? You call it what? A.
Why you call this one?
B so that you will not miss out 2 by 2 is five A you press five and we are considering this as a abn 1 = 1 = 0 = 0 = follow instruction 1 equal to you have put it in that AB then you press AC in your calculator have you press AC everything has appeared it's a lie everything has been saved in your calculator now when you press AC you have automatically saved it now to go for B you press shift Are you there? Four.
Because we are still getting the dimension. You press one for dimension.
Press one for dimension.
Then press two for M B.
Five again. Uh-huh.
You put one equal to 2 = 2 = 3 equal to also press AC to save it.
AC is to save it.
All right.
Now I want to find b ^ 2 - 4 b - i.
The question says 5 b ^ 2 - 4 b - i.
I'll press my calculator. Shift the following instruction.
Shift. Are you there?
Four.
Matrix B. Go to four. That has matrix B.
Press four. Can you see M there squared? Your normal square. Now press S that S square there. So you have M B square. Do you have it in your phone?
What is this?
>> You press minus four.
You go again.
You press shift four.
This time around, you still press M which is four, right?
Do you see in your in your calculator as I'm talking to you M B² - 4 M B >> in your calculator?
>> Yes. minus this is I minus shift 4.
Which symbol has I? A. Which number has symbol A? Three. You press it. You see my minus mark A.
We are done. Press equal to. You get zero. Check it.
Did you guys >> This is how it is.
They will not change it.
>> The good news is that it's good you know it.
It's good. You know how to press it.
It's calculator. You have 25 minutes for mathematics for 35 questions. Listen, the computer time wrong with speed of light.
The one you experience in chemistry and other subjects. Biology is learning in computer time for mathematics.
Especially for those I say somebody can just solve only four question and it's done in mathematics.
Why? Who are those people that solve only four question and the time is up?
When you are solving what you don't know you see number one I know it you start solving 10 minutes is out you are still in number one or 5 minutes is out you are still in number one. You enter number two before you enter number three or four. Time up.
20 minutes 5 minutes for one question.
Four question you are done. This is reality. Tomorrow you experience it.
But if you are smart, if you are smart, very smart, not only with calculator, smart in your brain. If you see this question and you have seen it here or in telegram, what you do is finish up first within a short period of time before you help anybody around you.
Then start confirming with your calculator.
Anyone you can easily retreat, you click again. A one you want to change, you can easily change it now. But when you don't have time to go through it again, how will YOU CHANGE IT? WHERE you are busy solving what you don't know. The worst thing is that when you finish solving, you will not see the answer.
>> But that is the fact you will solve because of minor sign you will not see the answer. Okay? So please I want you to focus on what I'm giving you. disease from those all those questions you are saying running up and I have all of them but I packed them and kept them somewhere I have all of them but I'm doing the needful you remember when I when I was doing some revision with you it was at night I started bringing them posting them and giving you the answer just for formality and just to clear things with you when you are not organized yourself will be a problem itself You need to organize yourself while writing exam, while preparing for exam.
Reason why it be as if you go to exam hall, you see what I have given to you.
If I were to be in your exam in your shoe, I am going for the exam. Will it be difficult for me? The way I'm preparing you is where I'm supposed to prepare. So the way it is easier for you.
Thank you.
When you are through with this, press I want to give you the shortest way on how to get your answer when you are finding determinant.
Press shift fast.
Press shift. Have you done that?
Press four.
Have you done that? If you look at calculator very well, you will see seven there. Right? Press seven.
Can you see that there?
Press shift again.
Press four.
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