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Let L : P, → P3 be the lincar transformation defined by L(ax² + bx + c) = (a – b + c)x² (2b + c)x + (2a + 3c). (a) Verify that B = {r² – 1,x + 1, x} is a basis for P3. (b) Find the matrix representation of L with respect to the basis B. (c) Find a basis for Ker L. (d) Find a basis for Im(L).

Let L : P, → P3 be the lincar transformation defined by L(ax² + bx + c) = (a – b + c)x² (2b + c)x + (2a + 3c). (a) Verify that B = {r² – 1,x + 1, x} is a basis for P3. (b) Find the matrix representation of L with respect to the basis B. (c) Find a basis for Ker L. (d) Find a basis for Im(L).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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→ P3 be the lincar transformation defined by L(ax² + bx + c) = (a – b+ c)x² - Let L: P3 (2b + c)x + (2a + 3c). (a) Verify that B = {x² – 1, x + 1, x} is a basis for P3. (b) Find the matrix representation of L with respect to the basis B. (c) Find a basis for Ker L. (d) Find a basis for Im(L).
Transcribed Image Text:→ P3 be the lincar transformation defined by L(ax² + bx + c) = (a – b+ c)x² - Let L: P3 (2b + c)x + (2a + 3c). (a) Verify that B = {x² – 1, x + 1, x} is a basis for P3. (b) Find the matrix representation of L with respect to the basis B. (c) Find a basis for Ker L. (d) Find a basis for Im(L).
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