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Let W be the set of all vectors of the form shown on the right, where b and care arbitrary. Find vectors u and v such that

Let W be the set of all vectors of the form shown on the right, where b and care arbitrary. Find vectors u and v such that

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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Let W be the set of all vectors of the form shown on the right, where b and c are arbitrary. Find vectors u and v such that W = Span{u, v). Why does this show that W is a subspace of R³? Using the given vector space, write vectors u and v such that W = Span{u, v}. {u, v} = (Use a comma to separate answers as needed.) Choose the correct theorem that indicates why these vectors show that W is a subspace of R³. 4b-7c -b 4c O A. The null space of an mxn matrix is a subspace of R". Equivalently, the set of all solutions to a system Ax = 0 of m homogeneous linear equations in n unknowns is a subspace of R OB. The column space of an mxn matrix A is a subspace of Rm. O C. An indexed set (V₁Vp) of two or more vectors in a vector space V, with v₁ #0 is a subspace of V O D. If v₁....,Vp are in a vector space V, then Span (V₁....Vp) is a subspace of V. and only if some v; is in Span {V₁V₁-1Vj}.
Transcribed Image Text:Let W be the set of all vectors of the form shown on the right, where b and c are arbitrary. Find vectors u and v such that W = Span{u, v). Why does this show that W is a subspace of R³? Using the given vector space, write vectors u and v such that W = Span{u, v}. {u, v} = (Use a comma to separate answers as needed.) Choose the correct theorem that indicates why these vectors show that W is a subspace of R³. 4b-7c -b 4c O A. The null space of an mxn matrix is a subspace of R". Equivalently, the set of all solutions to a system Ax = 0 of m homogeneous linear equations in n unknowns is a subspace of R OB. The column space of an mxn matrix A is a subspace of Rm. O C. An indexed set (V₁Vp) of two or more vectors in a vector space V, with v₁ #0 is a subspace of V O D. If v₁....,Vp are in a vector space V, then Span (V₁....Vp) is a subspace of V. and only if some v; is in Span {V₁V₁-1Vj}.
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