E and C= ( Lienly ndependent vectors in he -5 3 The two lists B = of linearly independent vectors in the -2 vector space M2×2 of all 2 × 2 matrices actually both form bases for the same vector subspace V of M2x2- a. Find the change of coordinates matrix from C to B. PBC = b. M is an element of V. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is [M]c= [M]B= c. Find M. М —
E and C= ( Lienly ndependent vectors in he -5 3 The two lists B = of linearly independent vectors in the -2 vector space M2×2 of all 2 × 2 matrices actually both form bases for the same vector subspace V of M2x2- a. Find the change of coordinates matrix from C to B. PBC = b. M is an element of V. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is [M]c= [M]B= c. Find M. М —
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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Question
![=G 9: and c =<,L rimenly independent vectos in the
[-5
3
1
) and C =
of linearly independent vectors in the
3
vector space M2x2 of all 2 x 2 matrices actually both form bases for the same vector subspace V of M2x2.
a. Find the change of coordinates matrix from C to B.
PB-C=
b. M is an element of V. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is
[M]c=
3
[M]B=
c. Find M.
M =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2454b861-4eec-41db-9c48-ef4eb24a952e%2F1e07e034-a5f2-46d4-935b-fd9ad1a28c3b%2Fy7jbp2_processed.png&w=3840&q=75)
Transcribed Image Text:=G 9: and c =<,L rimenly independent vectos in the
[-5
3
1
) and C =
of linearly independent vectors in the
3
vector space M2x2 of all 2 x 2 matrices actually both form bases for the same vector subspace V of M2x2.
a. Find the change of coordinates matrix from C to B.
PB-C=
b. M is an element of V. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is
[M]c=
3
[M]B=
c. Find M.
M =
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