Question

help needed in this matrix question : drawing wait for that

Answer 1

i am drawing wait

Answer 2

Could you post it as a drawing here on the site or using the equation editor please?

Answer 3

ok will screenshot work ?

Answer 4

that would also work.

Answer 5

is it working @KingGeorge

Answer 6

Thanks for the screenshot. Give me a minute to see what I get.

Answer 7

k no problem

Answer 8

@KingGeorge i want this to be done through taking 2AB = 0

Answer 9

if you used the fact that (a+b)^2 = a^2+2ab+b^2, you are assuming that matrices commute, which is not the case.

Answer 10

With matrices you should get:\[(A+B)^2=A^2+AB+BA+B^2\]

Answer 11

\[
(A+B)^2=\left(
\begin{array}{cc}
(a+1)^2 & 0 \\
(a+1) (b+2)-2 (b+2) & 4 \\
\end{array}
\right)=\\
A^2+B^2=\left(
\begin{array}{cc}
a^2+b-1 & a-1 \\
a b-b & b \\
\end{array}
\right)
\]

Answer 12

So we want \(AB=-BA\). If we do these multiplications, we get that \[AB=\left[\begin{matrix} a-b & 2 \\ 2a-b & 3\end{matrix}\right]\]and \[-BA=\left[\begin{matrix} 2-a & a+1 \\ 2-b& b-1\end{matrix}\right]\]Remember that matrices are not commutative.

Answer 13

Solving the equations above
gives a=1, b=4

Answer 14

oh yes thanks a lot every one it is a tough situaton for me to give medal to whom :(

Answer 15

I like @KingGeorge solution more than mine.

Answer 16

thanks all

Answer 17

Your's is a little more explicit about it though.

Answer 18

I forgot a negative in one of my my matrices :( It should have been \[-BA=\left[\begin{matrix} -2-a & a+1 \\ 2-b& b-1\end{matrix}\right]\]

Answer 19

help me here king
http://openstudy.com/study#/updates/4fbc67f0e4b05565343170c1