show that the set D={A element of M22(2*2 matrices)|Tr(A)=0} is a subspace of M22........Tr(A) is the trace of matrix A ,by the trace of matrix we mean the sum of the element in the main diagonal.

Question

turingtest · Answer

$$A=\left[\begin{matrix}a&b\c&-a\end{matrix}\right]$$

turingtest · Answer

again we need to show closure under addition, multiplication, and find a zero vector

turingtest · Answer

what part exactly are you having trouble with?

turingtest · Answer

$$B=\left[\begin{matrix}x&y\z&-x\end{matrix}\right]$$find $A+B$ and $AB$ and see if that is in $D$

anonymous · Answer

does the closure with respect to scalar multiplication hold?

anonymous · Answer

ohhh it does hold ..thanks