Given two bases B = {(1, 1,2), (1, 2, 3), (1, 6, 6)} V1 V2 ...

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Given two bases B = {(−1, −1,2), (−1, −2, 3), (1, −6, 6)} V1 V2 ալ and C = {(1,−1,−1), (−1, −1, 1), (1, −2,1)} V3 U2 Uz of R³, (i) find the change of coordinates (transition) matrix Mc = R³×³ from the coordinates with respect to C to the coordinates with respect to B, (ii) find the coordinates [p(x)]ß € R³ and [p(x)]c € R³ of p(x) = 3x² − x + 4 € P3, with respect to B and C, (iii) verify the equality ßMc[p(x)]c = [p(x)]ß. Justify your answer! Given two bases B = {(−1, −1,2), (−1, −2, 3), (1, −6, 6)} V1 V2 ալ and C = {(1,−1,−1), (−1, −1, 1), (1, −2,1)} V3 U2 Uz of R³, (i) find the change of coordinates (transition) matrix Mc = R³×³ from the coordinates with respect to C to the coordinates with respect to B, (ii) find the coordinates [p(x)]ß € R³ and [p(x)]c € R³ of p(x) = 3x² − x + 4 € P3, with respect to B and C, (iii) verify the equality ßMc[p(x)]c = [p(x)]ß. 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 the full answer