12. Let V denote the set of all solutions to the system of linear equations X1 X2 +2x43x5 + x6 = 0 2x1 - x2 - - x3 3x4 4x5 + 4x6 = 0. (a) Show that S = {(0, -1, 0, 1, 1, 0), (1, 0, 1, 1, 1, 0)} is a linearly inde- pendent subset of V. (b) Extend S to a basis for V.
12. Let V denote the set of all solutions to the system of linear equations X1 X2 +2x43x5 + x6 = 0 2x1 - x2 - - x3 3x4 4x5 + 4x6 = 0. (a) Show that S = {(0, -1, 0, 1, 1, 0), (1, 0, 1, 1, 1, 0)} is a linearly inde- pendent subset of V. (b) Extend S to a basis for V.
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter5: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 5CC
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Section 3.4:Number 12
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