Determinants Problem: how to solve the AA^2

[tonakis]

Well this is my first time here, I don't want to be the leech of the forums but I am trying to study for my examination next month and I haven't progressed much. I am trying to find an example of how to solve this mathematic problem. I am completely unaware of how to solve the AA^2 and the rest below and I do not even know what to read in order to understand it better. The teacher doesn't give any examples whatsoever how the letters bellow are solved. I am stuck...

 

[Steven G]

Well this is my first time here, I don't want to be the leech of the forums but I am trying to study for my examination next month and I haven't progressed much. I am trying to find an example of how to solve this mathematic problem. I am completely unaware of how to solve the AA^2 and the rest below and I do not even know what to read in order to understand it better. The teacher doesn't give any examples whatsoever how the letters bellow are solved. I am stuck...

In AA² you are being asked to multiply two matrices, namely A and A², where Aⁿ=A*A*...*A (where there are n A's). So A²=AA.

 

[tonakis]

So basically AA^2 is A*A*A?
Calculating the first determinant I should be getting the result -2x if we do 0*1-2*x right?
If i'm correct AA^2 should be -8x^3

 

[pka]

=tonakis;398782]I am completely unaware of how to solve the AA^2 and the rest below and I do not even know what to read in order to understand it better. The teacher doesn't give any examples whatsoever how the letters bellow are solved. I am stuck...

I am at almost complete loss trying to understand the purpose of this question.
\(\displaystyle A^2\begin{pmatrix} 2x & 2 \\ x & 2x+1\end{pmatrix} \) & \(\displaystyle A\cdot A^2=A^2\cdot A=A^3=\begin{pmatrix} 2x & 4x+2 \\ 2x^2+x & 4x+1\end{pmatrix} \)

However, none of \(\displaystyle C\cdot B,~A+B,~B^2\) exists.

I have no idea what \(\displaystyle B/C\) could mean.

 

[Deleted member 4993]

In AA² you are being asked to multiply two matrices, namely A and A², where Aⁿ=A*A*...*A (where there are n A's). So A²=AA.

However, B² [not a square matrix], B+A [B and A do not have same rank] and B/C {matrix division ??} does not make sense.....

edit: OKay, pka beat me to it....

 

[tonakis]

If these do not exist then how come he needs an answer for them? I tried doing B^2 but i don't think that's even possible. That's why I'm asking here if there's a solution to this problem, he is a teacher he can't be wrong, I think. That's exactly one of the examination's problems we need to solve. I have 6 subjects to pass and I'll get my certificate, these stand in my way...

 

[Steven G]

If these do not exist then how come he needs an answer for them? I tried doing B^2 but i don't think that's even possible. That's why I'm asking here if there's a solution to this problem, he is a teacher he can't be wrong, I think. That's exactly one of the examination's problems we need to solve. I have 6 subjects to pass and I'll get my certificate, these stand in my way...

You can NOT multiply matrices if they are not of the correct size. You can NOT square or cube a matrix if it is not a square matrix. Many volunteers on this site are true mathematicians who I will listen to over any 'teacher'. Possibly your teacher is not wrong but rather your teacher is testing to see if you know that the problem can't be done. If you do not believe what people on this forum are telling you then the forum really can't help you. Personally I would like for you to stay around and get help as you need it and even volunteer to answer some posts that you feel comfortable answering. Good luck.

 

[tonakis]

You can NOT multiply matrices if they are not of the correct size. You can NOT square or cube a matrix if it is not a square matrix. Many volunteers on this site are true mathematicians who I will listen to over any 'teacher'. Possibly your teacher is not wrong but rather your teacher is testing to see if you know that the problem can't be done. If you do not believe what people on this forum are telling you then the forum really can't help you. Personally I would like for you to stay around and get help as you need it and even volunteer to answer some posts that you feel comfortable answering. Good luck.

My post wasn't meant to be offensive, I believe you guys over my teacher that's for sure, I'm very sorry if it came out like that. I really appreciate everyone's efforts trying to help me out with these as I am trying to understand what this moron, sorry for the word, wants from my life.

In any case, I've writeen down the AA^2 and I got the result: -8x^2

I am at almost complete loss trying to understand the purpose of this question.
\(\displaystyle A^2\begin{pmatrix} 2x & 2 \\ x & 2x+1\end{pmatrix} \) & \(\displaystyle A\cdot A^2=A^2\cdot A=A^3=\begin{pmatrix} 2x & 4x+2 \\ 2x^2+x & 4x+1\end{pmatrix} \)

However, none of \(\displaystyle C\cdot B,~A+B,~B^2\) exists.

I have no idea what \(\displaystyle B/C\) could mean.

is that an example of the AA^2 solution?
Could division be applied at the B/C? (prolly a stupid question)

 

[pka]

My post wasn't meant to be offensive, I believe you guys over my teacher that's for sure, I'm very sorry if it came out like that. I really appreciate everyone's efforts trying to help me out with these as I am trying to understand what this moron, sorry for the word, wants from my life.

In any case, I've writeen down the AA^2 and I got the result: -8x^2


is that an example of the AA^2 solution?
Could division be applied at the B/C? (prolly a stupid question)

The determinant \(\displaystyle |A^3|=-8x^2\).
The actual products, is what I gave you.
Except for \(\displaystyle BC=\begin{pmatrix} 11\\4 \end{pmatrix} \)

Only square matrices have determinants

 

[tonakis]

Great that's very helpful! I even managed to do AA^2 by myself. I'll ask the teacher about the BC type. Because I believe the correct answer is the one you gave me: Only square matrices have determinants
and that's what I would've answered if the day came. Thanks again guys!

 

[tonakis]

To answer my own question, it's not a determinant, it's what the example suggests, a multiplication of matrices which means AA²= A³

 

[Deleted member 4993]

To answer my own question, it's not a determinant, it's what the example suggests, a multiplication of matrices which means AA² should be |9 6| ?
.................................................................................................................................................................................... . ...............|0 0|...............Incorrect

Look at the 4th post in this thread (by pka).

 

[tonakis]

I see what you mean and now I understand which solution is the correct one thanks for helping once again mr Khan.