# kernel of a set of matrices

• Dec 16th 2012, 08:50 PM
bonfire09
kernel of a set of matrices
I have to show 0= T(A)=A+A^T
A=[a b].
///[c d]

I got it to where [2a c+b]=[0 0]
///////////////////[b+c 2d]//[0 0]

I know a=d=0 and b=-c. but then i can seem to figure out why the answer is
ker T={[0 -b]
////////[b 0] where b is a real number}
how do they get that?
• Dec 16th 2012, 09:08 PM
Deveno
Re: kernel of a set of matrices
would it make more sense to you if they used "c" instead of "b"? it's just a place-holder, any symbol could have been used.
• Dec 16th 2012, 09:25 PM
bonfire09
Re: kernel of a set of matrices
Oh OK. I get that its just placeholders but since c=-b the wouldn't it just be [0 -b][-b 0]?
• Dec 16th 2012, 09:33 PM
Deveno
Re: kernel of a set of matrices
the upper-right (1,2)-entry must be the NEGATIVE of the (2,1)-entry, so:

$\displaystyle \begin{bmatrix}0&-b\\-b&0 \end{bmatrix}$

won't work. change one of those b's to a positive one and you have a winner.
• Dec 16th 2012, 09:39 PM
bonfire09
Re: kernel of a set of matrices
Oh got it. Thanks I figured out why. It has to satisfy A+A^T=0.