B₁ = {V₁, V2, V3} and B₂ = {w₁, W2, W3} be ordered bases of R³. The change of basis matrix from Co B₁ is [213] P = 0 1 2 [103] Write w₁ - w₂ + 2w3 as a linear combination of V1, V2, V3. Determine P-1 using elementary row operations. Suppose f: R³ R³ is the linear transformation such that f(v1) = 2v1 + v3, f(v₂) = v2 +2v3, f(v3) = v1 + 2v2. Find the matrix representation A off with respect to B₁.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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IV. Let B₁ = {V₁, V2, V3} and B₂ = {w₁, w2, w3} be ordered bases of R³. The change of basis matrix from
B₂ to B₁ is
[213]
P = 0 1 2
[103]
1. Write w₁ w₂ + 2w3 as a linear combination of v₁, U2, U3.
2. Determine P-1 using elementary row operations.
3. Suppose f: R³
R³ is the linear transformation such that
f(v1) = 2v1 + v3, f(v2) = v2 +2v3, f(v3) = v₁ + 2v2.
Find the matrix representation A off with respect to B₁.
4. What is the matrix representation C of f with respect to B₂?
Transcribed Image Text:IV. Let B₁ = {V₁, V2, V3} and B₂ = {w₁, w2, w3} be ordered bases of R³. The change of basis matrix from B₂ to B₁ is [213] P = 0 1 2 [103] 1. Write w₁ w₂ + 2w3 as a linear combination of v₁, U2, U3. 2. Determine P-1 using elementary row operations. 3. Suppose f: R³ R³ is the linear transformation such that f(v1) = 2v1 + v3, f(v2) = v2 +2v3, f(v3) = v₁ + 2v2. Find the matrix representation A off with respect to B₁. 4. What is the matrix representation C of f with respect to B₂?
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