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August 20th, 2017, 06:37 PM   #1
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Exercises of matrices algebra.

Hey guys, I need help. I have a homework and there are 3 exercises that I just can't do and I don't know how to proceed.

1. Let A and B.

$\displaystyle A= \begin{bmatrix} a && b \\ c && d \end{bmatrix} B= \begin{bmatrix} x && y \\ y && z \end{bmatrix}$

Find if it is possible, giving conditions in each case.
-> The matrices sum $\displaystyle A+B$, such that $\displaystyle A+B = (A^{-1} + B^{-1}) ^ T$

2. Simplify as little as possible each of the following matrix expressions.

$-2A^{-2}(A^{-2} + A^{-3})^{-1} + 2A^3(A^2 + A^3)^{-1} + \dfrac34A(A^{-1} + I)^{-1} + \dfrac34A^3(A + I)^{-1}$

3. If $A^2 - 2I + A = 0$

$4(A + I)^3 + 3(I - A^{-1})^2+ 2(4A - 2I + 3A^{-1}) =\ .....A\, +\ .....I\, +\ .....A^{-1}$

Expand the remarkable products so that you know what information you need, find the information you need and finally replace what you found in the remarkable products; When you clear $A^{-2}$ use the expression that is in terms of $A^{-1}$ and $I$.

$I$ = identity

Help me with what you can, 1, 2 or 3. Any help is received, sorry for my English.

Thanks!

Last edited by skipjack; August 21st, 2017 at 01:17 AM.
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August 21st, 2017, 01:34 AM   #2
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2. The first two expressions cancel. Write the remaining two with a common factor of $\dfrac34A^2$, etc.

3. Can you make an attempt and post what you can do?
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August 21st, 2017, 07:25 AM   #3
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Quote:
Originally Posted by skipjack View Post
2. The first two expressions cancel. Write the remaining two with a common factor of $\dfrac34A^2$, etc.

3. Can you make an attempt and post what you can do?

Hey, thanks for your answer.

2. Yes, the first two expressions cancel. But I don't know how to write the remaining with a common factor of . Can you explain me?

I got this:



3. I have it already.

Last edited by syncstar; August 21st, 2017 at 07:34 AM.
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September 24th, 2017, 04:14 AM   #4
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"Simplify as little as possible"?
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September 24th, 2017, 05:16 AM   #5
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That's Google Translate for you.
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