3. Let B= b₁ b2 b3 be a basis for R3 and let v = (a) Find [v], the coordinate vector of v with respect to the B-basis. R₁-R2 R₂-R3 00 2 01 0 " [v]B] (b) Suppose T: R3 R2 is the linear transformation satisfying T(b₁) = [52] = [2] T(b₂)= | [21]. T(bs) = ====== [3] Find T(v). HINT: IN PART (a) YOU FOUND THE COORDINATES OF v. WHAT ARE THOSE COORDINATES ACTUALLY COMMUNICATING TO YOU ABOUT THE RELATIONSHIP BETWEEN V AND B?

3. Let B= b₁ b2 b3 be a basis for R3 and let v = (a) Find [v], the coordinate vector of v with respect to the B-basis. R₁-R2 R₂-R3 00 2 01 0 " [v]B] (b) Suppose T: R3 R2 is the linear transformation satisfying T(b₁) = [52] = [2] T(b₂)= | [21]. T(bs) = ====== [3] Find T(v). HINT: IN PART (a) YOU FOUND THE COORDINATES OF v. WHAT ARE THOSE COORDINATES ACTUALLY COMMUNICATING TO YOU ABOUT THE RELATIONSHIP BETWEEN V AND B?

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 3CM: Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions...

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