Answer to Question #44643 in Linear Algebra for Anurodh

Question

Let T : R^2 - R^2 and S: R^2 - R^2 be linear operators defined by
T (x1;x2) = (x1+x2, x1-x2) and S(x1;x2) = (x1, x1+2x2)
respectively.
i) Find T ◦ S and S ◦ T.
ii) Let B = f(1, 0), (0, 1) be the standard basis of R^3. Verify that
[T ◦ S]B = [T]B ◦ [S]B.