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 linear combination of u and v. %3D !!

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 linear combination of u and v. %3D !!

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 13CR

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Consider the vectors u = (1,2,3) and v= (2, 3, 1) in R³.
(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 linear combination of u and v.
(d) Find conditions on a, b, c so that w = (a,b,c) is a linear combination of u and v.

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