Finding the standard matrix for the linear transformation: T:R^2 --- R^2 reflects a vector about the line y=-x, then projects that vector onto the y axis and then compresses that vector by a factor of 0.5 in the y direction?

Question

Finding the standard matrix for the linear transformation: T:R^2 ---> R^2 reflects a vector about the line y=-x, then projects that vector onto the y axis and then compresses that vector by a factor of 0.5 in the y direction?

anonymous · Answer

I was also wondering if it's possible to have a different codomain and domain when doing this like T:R^2---> R^3?

anonymous · Answer

T(1, 0) = (0, -0.5)
T(0, 1) = (0, 0)

anonymous · Answer

$$ \left[ \begin {array}{cc} 0&0\ -1/2&0\end {array}
 \right] $$