Let L be the linear transformation on R3 defined by L(x) = 2x1 x2 x3 2x2 x1 x3 2x3 x1 x2
Chapter 4, Problem 3(choose chapter or problem)
Let L be the linear transformation on R3 defined by L(x) = 2x1 x2 x3 2x2 x1 x3 2x3 x1 x2 and let A be the standard matrix representation of L (see Exercise 4 of Section 2). If u1 = (1, 1, 0)T , u2 = (1, 0, 1)T , and u3 = (0, 1, 1)T , then {u1, u2, u3} is an ordered basis for R3 and U = (u1, u2, u3) is the transition matrix corresponding to a change of basis from {u1, u2, u3} to the standard basis {e1, e2, e3}. Determine the matrix B representing L with respect to the basis {u1, u2, u3} by calculating U1AU.
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