Question: Need help 1-3 (1) Let B be the following basis of R3: (0.1) If a = find [x] B. (2) Let B : 2 i

Need help 1-3

(1) Let B be the following basis of R3: (0.1) If a = find [x] B. (2) Let B : 2 i M2x2 denote the vector space of 2 x 2 matrices, and f : M2x2 -> M2x2 be the function f(A) = AB. Let B be the following basis of M2x2: Find [f (Ell)]B, [f(E12)]B, If(E21)]B, and [f (E22)]B. (3) What is the rank of the function f? Explain your reasoning (Hint: in R", you can compute the rank of a function by row-reducing the matrix [f(e1) ... f(en)] and counting pivots. Here, the idea is to use the B-coordinate vectors of f applied to the basis elements.)

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