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{1+2t – t3,3 +t+4t2, 6t2 + 263, 4 – 5t2} (b) B = {1 – 212, 2t + 31, 2 + 3t – 3t2, -1 – t+t? + 31³} (a) B = 3. In one of your answers in (2), you should have proven some set, say B, was a basis for P3. For this basis B, determine the change of basis matrix [I]BA from the standard basis A := Also determine the change of basis matrix [I] AB from B to A. (You may find the matrices in whichever order is more convenient, but clearly say which matrix is which. And, as always, explain/show how you arrived at your answers.) {1, t, t2, t³} for P3 to B.

{1+2t – t3,3 +t+4t2, 6t2 + 263, 4 – 5t2} (b) B = {1 – 212, 2t + 31, 2 + 3t – 3t2, -1 – t+t? + 31³} (a) B = 3. In one of your answers in (2), you should have proven some set, say B, was a basis for P3. For this basis B, determine the change of basis matrix [I]BA from the standard basis A := Also determine the change of basis matrix [I] AB from B to A. (You may find the matrices in whichever order is more convenient, but clearly say which matrix is which. And, as always, explain/show how you arrived at your answers.) {1, t, t2, t³} for P3 to B.

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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(a) B = {1+2t – t³,3+t +4t2, 6t2 + 2t3, 4 – 5t2} (b) B = {1 – 212, 2t + 3t°, 2+ 3t – 312, -1 - t+ t2 + 3t} 3. In one of your answers in (2), you should have proven some set, say B, was a basis for P3. For this basis B, determine the change of basis matrix [I]BA from the standard basis A := Also determine the change of basis matrix [1] AB from B to A. (You may find the matrices in whichever order is more convenient, but clearly say which matrix is which. And, as always, explain/show how you arrived at your answers.) : {1,t, t2, t³ } for P3 to B.
Transcribed Image Text:(a) B = {1+2t – t³,3+t +4t2, 6t2 + 2t3, 4 – 5t2} (b) B = {1 – 212, 2t + 3t°, 2+ 3t – 312, -1 - t+ t2 + 3t} 3. In one of your answers in (2), you should have proven some set, say B, was a basis for P3. For this basis B, determine the change of basis matrix [I]BA from the standard basis A := Also determine the change of basis matrix [1] AB from B to A. (You may find the matrices in whichever order is more convenient, but clearly say which matrix is which. And, as always, explain/show how you arrived at your answers.) : {1,t, t2, t³ } for P3 to B.
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