Suppose V1, V2, V3, V4, V5 are distinct, nonzero vectors in R³ = and suppose that span(V1, V2, V3, V4, V5 ) — span(v₁, v5) and that vå and v5 are scalar multiples. Which of the following statement MUST be TRUE? Select all that apply. Each of the vectors 4, 5 is a linear combination of the vectors V₁, V2, and V3. span (v1, U2, V3) = span (v4, 25). If we form a matrix A, with the vectors U1, U2, U3, V4, v5 as columns, then the system Ax = 0 has a nonzero solution. There are more vectors than elements in each vector. So if we set up a system of equations we will have more variables than equations (more columns than rows in the matrix A). From this we can conclude that the equation Ax=0 will have a non- trivial solution. Each of the vectors ₁, ₂, 3 is a linear combination of the vectors, and us. span(v1, U2, U3, U4, 5) is a plane.
Suppose V1, V2, V3, V4, V5 are distinct, nonzero vectors in R³ = and suppose that span(V1, V2, V3, V4, V5 ) — span(v₁, v5) and that vå and v5 are scalar multiples. Which of the following statement MUST be TRUE? Select all that apply. Each of the vectors 4, 5 is a linear combination of the vectors V₁, V2, and V3. span (v1, U2, V3) = span (v4, 25). If we form a matrix A, with the vectors U1, U2, U3, V4, v5 as columns, then the system Ax = 0 has a nonzero solution. There are more vectors than elements in each vector. So if we set up a system of equations we will have more variables than equations (more columns than rows in the matrix A). From this we can conclude that the equation Ax=0 will have a non- trivial solution. Each of the vectors ₁, ₂, 3 is a linear combination of the vectors, and us. span(v1, U2, U3, U4, 5) is a plane.
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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Transcribed Image Text:Suppose V1, V2, V3, V4, V5 are distinct, nonzero vectors in R³
and suppose that span(V1, V2, V3, V4, V5) = span (V4, V5) and that v4 and v5 are not
scalar multiples.
Which of the following statement MUST be TRUE? Select all that apply.
Each of the vectors 4, 5 is a linear combination of the vectors V1, V2, and v3.
span(V1, V2, V3) = span (v4, 25).
✔
If we form a matrix A, with the vectors V₁, V2, V3, V4, V5 as columns, then the
system Ax
0 has a nonzero solution.
=
There are more vectors than elements in each vector. So if we set up a system of
equations we will have more variables than equations (more columns than rows in
the matrix A). From this we can conclude that the equation Ax=0 will have a non-
trivial solution.
Each of the vectors ₁, 2, 3 is a linear combination of the vectors, and us.
span(v1, v2, U3, U4, U5) is a plane.
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