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12 Nov 2019
Suppose that W is a four dimensional vector space with basis S = {v_1, v_2, v_3, v_4}. (a) Argue that B = {b_1, b_2, b_3, b_4} is also a basis for W, where b_1 = v_1 + v_2, b_2 = v_2 + v_3, b_3 = v_3 + v_4 and b_4 = v_4. (b) Find the change of basis matrix P from S to B, so that [x]_s = P[x]_s, for all x elementof W. (c) Find the change of basis matrix Q from B to S, so that [x]_s = Q[x]_s, for all x elementof W. (d) Calculate the product PQ to verify that P = Q^-1.
Suppose that W is a four dimensional vector space with basis S = {v_1, v_2, v_3, v_4}. (a) Argue that B = {b_1, b_2, b_3, b_4} is also a basis for W, where b_1 = v_1 + v_2, b_2 = v_2 + v_3, b_3 = v_3 + v_4 and b_4 = v_4. (b) Find the change of basis matrix P from S to B, so that [x]_s = P[x]_s, for all x elementof W. (c) Find the change of basis matrix Q from B to S, so that [x]_s = Q[x]_s, for all x elementof W. (d) Calculate the product PQ to verify that P = Q^-1.
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Irving HeathcoteLv2
5 Nov 2019