Given two bases {(-1,-1,2), (-1,-2,3), (1,-6,6)} U3 U1 U and = {(,-1,-1), 1-,1),(-,0)} U 22 U3...

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Given two bases {(-1,-1,2), (-1,-2,3), (1,-6,6)} U3 U1 U and = {(,-1,-1), 1-,1),(-,0)} U 22 U3 of R 3, (i) find the change of coordinates (transition) matrix ER 3 from the coordinates with respect to to the coordinates with respect to (ii) find the coordinates [p(x)] ER and [p(x)] ER of p(x) = 3x - x + 4 3, with respect to and, (iii) verify the equality [p(x)] = [p(x)]o. Given two bases {(-1,-1,2), (-1,-2,3), (1,-6,6)} U3 U1 U and = {(,-1,-1), 1-,1),(-,0)} U 22 U3 of R 3, (i) find the change of coordinates (transition) matrix ER 3 from the coordinates with respect to to the coordinates with respect to (ii) find the coordinates [p(x)] ER and [p(x)] ER of p(x) = 3x - x + 4 3, with respect to and, (iii) verify the equality [p(x)] = [p(x)]o.