Consider the vectors u = (1,2,3) and v= (2,3, 1) in R. (a) Write w = (1,3, 8) as a lincar combination of u and v. (b) Write w = (2, 4, 5) as a lincar combination of u and v. (c) Find k so that w = (1, k, 4) is a linear combination of u and .

Elementary Linear Algebra (MindTap Course List)
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Author:Ron Larson
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Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
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Consider the vectors u = (1,2,3) and v= (2, 3, 1) in R.
(a) Write w = (1,3, 8) as a linear combination of u and v.
(b) Write w = (2, 4, 5) as a linear combination of u and v.
(c) Find k so that w = (1, k, 4) is a lincar combination of u and v.
(d) Find conditions on a, b, c so that w = (a, b, c) is a lincar combination of u and v.
Transcribed Image Text:Consider the vectors u = (1,2,3) and v= (2, 3, 1) in R. (a) Write w = (1,3, 8) as a linear combination of u and v. (b) Write w = (2, 4, 5) as a linear combination of u and v. (c) Find k so that w = (1, k, 4) is a lincar combination of u and v. (d) Find conditions on a, b, c so that w = (a, b, c) is a lincar combination of u and v.
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