1. Let T: P2 → P3 be the linear transformation defined by T(p(x)) = xp(x). (a) Find the matrix for T relative to the sta

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1 Let T P2 P3 Be The Linear Transformation Defined By T P X Xp X A Find The Matrix For T Relative To The Sta 1 (25.21 KiB) Viewed 22 times

1. Let T: P2 → P3 be the linear transformation defined by T(p(x)) = xp(x). (a) Find the matrix for T relative to the standard bases where = {u₁, U2, U3} and B' = {V₁, V2, V3, V4} u₁=1, u₂=X, U3 = x V₁=1, V2=X, V3=x², V4=x² (b) Verify that the matrix [7] B', obtained in part (a) satisfies Formula 5 for every vector x=co+c₁x+c₂x² in P2