15. Let T: P₂M22 be the linear transformation defined by p(0) p(1)] T(p) = - P(-1) let B be the standard basis for M22, and let B' = {1, x, x²}, B" = {1,1 + x, 1 + x2} be bases for P2. a. Find [T]B, B and [T]B,B". b. For the matrices obtained in part (a), find T(2 + 2x + x²) using the three-step procedure illustrated in Example 2. c. Check the results obtained in part (b) by computing T(2 + 2x + x²) directly.
15. Let T: P₂M22 be the linear transformation defined by p(0) p(1)] T(p) = - P(-1) let B be the standard basis for M22, and let B' = {1, x, x²}, B" = {1,1 + x, 1 + x2} be bases for P2. a. Find [T]B, B and [T]B,B". b. For the matrices obtained in part (a), find T(2 + 2x + x²) using the three-step procedure illustrated in Example 2. c. Check the results obtained in part (b) by computing T(2 + 2x + x²) directly.
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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Please solve this question in handwrittting.
![DERM
15. Let T: P₂M22 be the linear transformation defined by
T(p) = -
p(0) p(1)]
P(-1)
let B be the standard basis for M22, and let B' = {1, x, x²},
B" = {1,1 + x, 1 + x2} be bases for P2.
a. Find [T]B, B and [T]B,B".
b. For the matrices obtained in part (a), find
T(2 + 2x + x²)
using the three-step procedure illustrated in Example 2.
c. Check the results obtained in part (b) by computing
T(2 + 2x + x²) directly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05419715-1bd0-4457-a143-03af22167dbf%2F36657245-9363-4df6-b7f4-b7188385c543%2Fp1f8e8s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:DERM
15. Let T: P₂M22 be the linear transformation defined by
T(p) = -
p(0) p(1)]
P(-1)
let B be the standard basis for M22, and let B' = {1, x, x²},
B" = {1,1 + x, 1 + x2} be bases for P2.
a. Find [T]B, B and [T]B,B".
b. For the matrices obtained in part (a), find
T(2 + 2x + x²)
using the three-step procedure illustrated in Example 2.
c. Check the results obtained in part (b) by computing
T(2 + 2x + x²) directly.
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