Consider the following vectors in R³. 1 = (1,0,4)^, 2 = (1,2,3)^, ūs = (2,2, 7)^, đa = (0, –2, 1)^, is = (0, 0, 1). (a) Given that R³ = span(ū₁, 2, 3, 4, ū5), reduce these vectors to a linearly independent set and hence form a basis for R³. (b) Write (x, y, z)¹ € R³ as a linear combination of the three vectors you obtained in (a).

Consider the following vectors in R³. 1 = (1,0,4)^, 2 = (1,2,3)^, ūs = (2,2, 7)^, đa = (0, –2, 1)^, is = (0, 0, 1). (a) Given that R³ = span(ū₁, 2, 3, 4, ū5), reduce these vectors to a linearly independent set and hence form a basis for R³. (b) Write (x, y, z)¹ € R³ as a linear combination of the three vectors you obtained in (a).

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 2CM: Take this test to review the material in Chapters 4and Chapters 5. After you are finished, check...

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