PassageLet T:R2→R3T:\mathbb{R}^2\to\mathbb{R}^3 be defined by T(x,y)=(x+y,x−y,3x+y)T(x,y)=(x+y,x-y,3x+y).
QuestionIf A=[abcdef]A=\begin{bmatrix}a&b\\c&d\\e&f\end{bmatrix} denotes the matrix of TT with respect to {(1,1),(1,−1)}\{(1,1),(1,-1)\} for R2\mathbb{R}^2 and {(1,1,1),(1,1,0),(−1,0,0)}\{(1,1,1),(1,1,0),(-1,0,0)\} for R3\mathbb{R}^3, what is a+d+ea+d+e?
