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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: 19,178 Thanks: 1646 
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? 
August 21st, 2017, 07:25 AM  #3  
Newbie Joined: Aug 2017 From: Earth Posts: 3 Thanks: 0  Quote:
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.  
September 24th, 2017, 04:14 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,244 Thanks: 887 
"Simplify as little as possible"?

September 24th, 2017, 05:16 AM  #5 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,330 Thanks: 2457 Math Focus: Mainly analysis and algebra 
That's Google Translate for you.


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