Question: Given two bases B = {(1, 1,2), (1, 2, 3), (1, 6, 6)} V1 V2 and C = {(1,1,1), (1, 1, 1), (1, 2,1)}

Given two bases B = {(1, 1,2), (1, 2, 3), (1, 6, 6)} V1 V2 and C = {(1,1,1), (1, 1, 1), (1, 2,1)} V3 U2 Uz of R, (i) find the change of coordinates (transition) matrix Mc = R from the coordinates with respect to C to the coordinates with respect to B, (ii) find the coordinates [p(x)] R and [p(x)]c R of p(x) = 3x x + 4 P3, with respect to B and C, (iii) verify the equality Mc[p(x)]c = [p(x)]. Justify your answer!

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To solve the given problem well proceed in several steps as outlined in the question i To find the change of coordinates transition matrix B MC we will write each vector of the basis C as a linear com... View full answer

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