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Question 4. Let Ei (6) . Ez- (0 ). ( 0).- (09) Let f: M2x2(R) + M2x2(R) be defined by f(A) = A - AT where AT, the transpose of A, is defined by (a)' = (a). You You may assume that f is linear. (a) Find the matrix (flê of f with respect to the bas

匿名用户 最后更新于 2021-12-01 19:08 数学类Mathematics

Question 4. Let Ei (6) . Ez- (0 ). ( 0).- (09) Let f: M2x2(R) + M2x2(R) be defined by f(A) = A - AT where AT, the transpose of A, is defined by (a)' = (a). You You may assume that f is linear. (a) Find the matrix (flê of f with respect to the basis E = E1, E2, E3, E4. (b) Find a basis for ker f. (c) Use the rank-nullity theorem to find dim im f. (d) Find a basis for im f.

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