2. Consider the transformation T : R¹ → R³ defined by - - - T(x1, x2, x3, x4) = (4x1 + x2 − 2x3 − 3x4, 2x1 + x2+x3 − 4x4,6×1 — 9x3 +9x4) (a) Find the matrix associated with this transformation. (b) Find a basis for ker(T). (c) Find a basis for Range (T). (d) Is T one-to-one? Why? (e) Is T onto? Why?

2. Consider the transformation T : R¹ → R³ defined by - - - T(x1, x2, x3, x4) = (4x1 + x2 − 2x3 − 3x4, 2x1 + x2+x3 − 4x4,6×1 — 9x3 +9x4) (a) Find the matrix associated with this transformation. (b) Find a basis for ker(T). (c) Find a basis for Range (T). (d) Is T one-to-one? Why? (e) Is T onto? Why?

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 25CM: Find a basis B for R3 such that the matrix for the linear transformation T:R3R3,...

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