8. Let S be the standard basis for R2, and let B = {v₁, v₂} be the basis in which v₁ = (2, 1) and v₂ = (-3, 4). (a) Find the transition matrix PB-s by inspection. (b) Use Formula (14) to find the transition matrix Ps B. (c) Confirm that PB s and PsB are inverses of one another. = (d) Let w (5, -3). Find [w]B and then use Formula (11) to compute [w]s. (e) Let w=(3, -5). Find [w] s and then use Formula (12) to compute [w]B.
8. Let S be the standard basis for R2, and let B = {v₁, v₂} be the basis in which v₁ = (2, 1) and v₂ = (-3, 4). (a) Find the transition matrix PB-s by inspection. (b) Use Formula (14) to find the transition matrix Ps B. (c) Confirm that PB s and PsB are inverses of one another. = (d) Let w (5, -3). Find [w]B and then use Formula (11) to compute [w]s. (e) Let w=(3, -5). Find [w] s and then use Formula (12) to compute [w]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
![8. Let S be the standard basis for R2, and let B = {v₁, v₂} be the
basis in which v₁ = (2, 1) and v₂ = (-3, 4).
(a) Find the transition matrix PBS by inspection.
(b) Use Formula (14) to find the transition matrix Ps B.
S→
(c) Confirm that PB s and PSB are inverses of one another.
(d) Let w = (5, -3). Find [w] B and then use Formula (11) to
compute [w]s.
(e) Let w
=
(3,-5). Find [w]s and then use Formula (12) to
compute [w]B.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe362d5a9-bcf1-4bcc-9808-2899b06de487%2Fa82b4a8d-f7cf-4147-aae8-7a33e592053c%2Fcjm9iei_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8. Let S be the standard basis for R2, and let B = {v₁, v₂} be the
basis in which v₁ = (2, 1) and v₂ = (-3, 4).
(a) Find the transition matrix PBS by inspection.
(b) Use Formula (14) to find the transition matrix Ps B.
S→
(c) Confirm that PB s and PSB are inverses of one another.
(d) Let w = (5, -3). Find [w] B and then use Formula (11) to
compute [w]s.
(e) Let w
=
(3,-5). Find [w]s and then use Formula (12) to
compute [w]B.
![(11) is
[V] B = PBB [V]B¹
(12) is (V)B'= PB-1B¹ [V] B
(14) is [new basus old basis]
row
operating
[Il transitam from old to new]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe362d5a9-bcf1-4bcc-9808-2899b06de487%2Fa82b4a8d-f7cf-4147-aae8-7a33e592053c%2Fnrxhl7b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(11) is
[V] B = PBB [V]B¹
(12) is (V)B'= PB-1B¹ [V] B
(14) is [new basus old basis]
row
operating
[Il transitam from old to new]
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