Answer to Question #288348 in Linear Algebra for Sabelo Xulu

Question

Q13.

Suppose T, S : R^2 $\to$ R^2 are linear defined by T (u, v) = (3u + v, u + 2v) and S (x, y) = (2x - y, x + y).

Also the matrices of T and S with respect to the standard bases of R^2 and R^2 are given as M (T) =$\begin{bmatrix} 3 & 1 \\ 1 & 2 \end{bmatrix}$

and M (S) =$\begin{bmatrix} 2 & - 1 \\ 1 & 1 \end{bmatrix}$. Then M(T S) =

(1) $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$

(2) $\begin{bmatrix} 3 & 1 \\ 1 & 5 \end{bmatrix}$

(3) $\begin{bmatrix} 3 & 1 \\ 4 & 1 \end{bmatrix}$

4) None of the given answers is true

Answer 1

M (T S) =$\begin{bmatrix} 3 & 1 \\ 1 & 2 \end{bmatrix}$$\begin{bmatrix} 2 & - 1 \\ 1 & 1 \end{bmatrix}$=$\begin{bmatrix} 7 & - 2 \\ 4 & 1 \end{bmatrix}$

Answer is (4) None of the given answers is true.