{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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![(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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90b663cb-622e-45de-96a3-0dc7a90c5f09%2F84f67979-9294-488c-9cb7-1337a058c4e2%2Fbg8goim_processed.jpeg&w=3840&q=75)
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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