1. Consider the transformation T : P2 R3 dened by T (p(t)) = p(0), p(1),...

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1. Consider the transformation T : P2 → R3 deﬁned by T (p(t)) =  p(0), p(1), p(2)   (3x1 matrix)

1a. Show that T is a linear transformation.

1b. Find the matrix for T relative to the bases B and E where B = {1, t, t2} and E = {e1, e2, e3}.

1c. Find a basis for the kernel of T . (Hint: this is another name for the null-space of the transformation.)

1d. Find the dimension of the range of T , and brieﬂy explain why this is the same as the rank of the matrix you found in 1b.

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Linear Algebra

ISBN: 9780982406212

1st Edition

Authors: Jim Hefferon

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Posted Date: Aug 16, 2022 08:28 AM

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1. Consider the transformation T : P2 R3 dened by T (p(t)) = p(0), p(1),...

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