d) Consider the linearly independent vectors (1, -2,3,-4) and (1, 1, 2, 2) in R¹. Ex- tend {(1, -2,3,-4), (1, 1, 2, 2)} to a basis S of R4 and find the matrix represen- tation of T: R4 → R², where T(x1, x2, x3, x₁) = (x₁ + x2, x3 + x₁), with respect to S and the basis {(1, 1), (0, 1)} of R².

d) Consider the linearly independent vectors (1, -2,3,-4) and (1, 1, 2, 2) in R¹. Ex- tend {(1, -2,3,-4), (1, 1, 2, 2)} to a basis S of R4 and find the matrix represen- tation of T: R4 → R², where T(x1, x2, x3, x₁) = (x₁ + x2, x3 + x₁), with respect to S and the basis {(1, 1), (0, 1)} of R².

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 8E

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