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?

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.

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]?

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.

Re: kernel of a set of matrices

Oh got it. Thanks I figured out why. It has to satisfy A+A^T=0.