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V is a vector space with bases B = (vị, V2, V3) and B' = (w1, w2, w3). The change of basis matrix from 1 1 2 B to B' is | 2 1 4 . Which of the following is [va]g ? 2 2 3 1 4 (3 8. 2. 2 1

V is a vector space with bases B = (vị, V2, V3) and B' = (w1, w2, w3). The change of basis matrix from 1 1 2 B to B' is | 2 1 4 . Which of the following is [va]g ? 2 2 3 1 4 (3 8. 2. 2 1

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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V is a vector space with bases B = (v1, v2, v3) and B' = 1, w2, W3). The change of basis matrix from 1 1 2 B to B' is | 2 1 4 Which of the following is [v2]g ? 2 2 3 1 2 1 4 8 2. 3.
Transcribed Image Text:V is a vector space with bases B = (v1, v2, v3) and B' = 1, w2, W3). The change of basis matrix from 1 1 2 B to B' is | 2 1 4 Which of the following is [v2]g ? 2 2 3 1 2 1 4 8 2. 3.
Expert Solution
Step 1

V is vector space with basis B={v1,v2,v3} and B'=w1,w2,w3

The change of basis matrix from basis B to B' is given.

Since, change of basis is from basis B to B' then elements of basis B is expressed in linear combination of basis B'

v1=aw1+bw2+cw3v2=a'w1+b'w2+c'w3v3=a''w1+b''w2+c''w3

Then change of matrix in general from basis B to basis B' is given as:

aa'a''bb'b''cc'c''

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