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 August 20th, 2017, 06:37 PM #1 Newbie   Joined: Aug 2017 From: Earth Posts: 3 Thanks: 0 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.
 August 21st, 2017, 01:34 AM #2 Global Moderator   Joined: Dec 2006 Posts: 19,739 Thanks: 1810 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? Thanks from syncstar
August 21st, 2017, 07:25 AM   #3
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Quote:
 Originally Posted by skipjack 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?

2. Yes, the first two expressions cancel. But I don't know how to write the remaining with a common factor of $\frac{3}{4}A^2$ . Can you explain me?

I got this:

$\frac{3}{4} (A^-^2+A^-^1)^-^1+\frac{3}{4}(A^-^3+A^-^2)$

Last edited by syncstar; August 21st, 2017 at 07:34 AM.

 September 24th, 2017, 04:14 AM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 "Simplify as little as possible"?
 September 24th, 2017, 05:16 AM #5 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,469 Thanks: 2499 Math Focus: Mainly analysis and algebra That's Google Translate for you.

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