Suppose the matrix A with column vectors V₁, V2, V3, V4 is row equivalent to the matrix C with column vectors W₁, W2, W3, W4. If W₁ = W₁-W₂ + 2w3, then which of the following statements MUST be TRUE? (Select all that apply) span(V₁, V2, V3, V4) = span(V₁, V2, V3) V₁ is in span(v2, V3, V4) span(V1, V2, V3, V4) = span(W₁, W2, W3, W4) V4 = V1 V2 + 2V3 as they are row equivalent dependency did not change span(W₁, W2, W3, W4) = span(w₁, W2, W3)
Suppose the matrix A with column vectors V₁, V2, V3, V4 is row equivalent to the matrix C with column vectors W₁, W2, W3, W4. If W₁ = W₁-W₂ + 2w3, then which of the following statements MUST be TRUE? (Select all that apply) span(V₁, V2, V3, V4) = span(V₁, V2, V3) V₁ is in span(v2, V3, V4) span(V1, V2, V3, V4) = span(W₁, W2, W3, W4) V4 = V1 V2 + 2V3 as they are row equivalent dependency did not change span(W₁, W2, W3, W4) = span(w₁, W2, W3)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 18EQ
Related questions
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![Suppose the matrix A with column vectors V₁, V2, V3, V4 is row equivalent to the
matrix C with column vectors W₁, W2, W3, W4. If W₁ = W₁-W₂ + 2w3, then
which of the following statements MUST be TRUE?
(Select all that apply)
span(V₁, V2, V3, V4) = span(V₁, V2, V3)
V₁ is in span (v2, V3, V4)
span(V1, V2, V3, V4) = span(w₁, W2, W3, W4)
✓ V4 = V1 V2 + 2V3
as they are row equivalent dependency did not change
span(W₁, W2, W3, W4)
=
span (w₁, W2, W3)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67ad69fc-d7b2-4082-8b18-7ae4b62544b8%2F2f7ab940-be64-4782-8981-705581c828cb%2Fna38gb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose the matrix A with column vectors V₁, V2, V3, V4 is row equivalent to the
matrix C with column vectors W₁, W2, W3, W4. If W₁ = W₁-W₂ + 2w3, then
which of the following statements MUST be TRUE?
(Select all that apply)
span(V₁, V2, V3, V4) = span(V₁, V2, V3)
V₁ is in span (v2, V3, V4)
span(V1, V2, V3, V4) = span(w₁, W2, W3, W4)
✓ V4 = V1 V2 + 2V3
as they are row equivalent dependency did not change
span(W₁, W2, W3, W4)
=
span (w₁, W2, W3)
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