Question

Which of the following is/are linear transformations ?

• A. T : $\R → \R$ given by T(x) = sin(x)
• B. T : $M_2(\R) → \R$ given by T(A) = trace(A)
• C. T : $\R^2 → \R$ given by T (x, y) = x + y + 1
• D. T : $P_2(\R) → \R$ given by T(p(x)) = p(1)

Answer 1

Answer: (B), (D)

T : $M_2(\R) → \R$ given by T(A) = trace(A)

Answer 2

The correct option is (B) : T : $M_2(\R) → \R$ given by T(A) = trace(A) and (D) : T : $P_2(\R) → \R$ given by T(p(x)) = p(1).