1. For each of the statements below, State whether it is true or false, and Motivate your answer with either a proof, a reference to a definition or theorem, or a counterexample. (a) Let A be an (m x...

please help me with 1a to d

Extracted text: 1. For each of the statements below, State whether it is true or false, and Motivate your answer with either a proof, a reference to a definition or theorem, or a counterexample. (a) Let A be an (m x n)-matrix. Write A := [v1 ... Vn] = W1 If {V1, V2} forms a basis for col(A), then {w1, W2} forms a basis for row (A). (b) Let A, B be (m x n)-matrices over R. If A and B are row equivalent, then row(A) row(B) and col(A) = col(B). (c) The set { [a 0 0] : a E R} is a l-dimensional subspace of R. 1 1 1 2 1 (d) Let A:= 1 and v := [1 2 2 1]. Then, u E col(A) and v row(A). ,u := 1 23