TRUE OR FALSE

SUBJECT: applied math

TRUE OR FALSE If the statement is TRUE, provide a justification. If the statement is FALSE, provide a counterexample. Suppose matrix A, and vectors x and y are conformable for the products Ax and Ay. If Ax and Ay are linearly independent, then a and y are linearly independent. If x and y are linearly independent, then Axe and Ay are linearly independent. If W1, W2, W2 are independent vectors, then v1 = W2 - W3 and v2 = W1 - Wg and v. = wj - w, are independent. V1 = W2 + W3 and v2 = W1+ W3 and vg = W1 + w2 are independent. If {w1, W2, W3} is a basis for subspace V, then {w2 - 3w1, 2w1 + w3, w2 + w2} is a basis for V