My Math Forum Exercises of matrices algebra.

 Linear Algebra Linear Algebra Math Forum

 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? Thanks from syncstar
August 21st, 2017, 07:25 AM   #3
Newbie

Joined: Aug 2017
From: Earth

Posts: 3
Thanks: 0

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: 3,244 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.

 Tags algebra, exercises, matrices

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post jack111 Linear Algebra 1 November 29th, 2014 12:31 AM Denis Linear Algebra 1 May 1st, 2013 03:14 PM john324 Real Analysis 3 December 19th, 2012 05:33 PM johnmath Advanced Statistics 1 March 5th, 2012 12:53 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top