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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Section 3.4:Number 12

12. Let V denote the set of all solutions to the system of linear equations X1 - X2 +2x43x5 + x6 = 0 2x1 x2 x3 + 3x44x5 + 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.
Transcribed Image Text:12. Let V denote the set of all solutions to the system of linear equations X1 - X2 +2x43x5 + x6 = 0 2x1 x2 x3 + 3x44x5 + 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.
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