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Let S = {[0, 1, −1, 2]T, [1, 2, 3, 0]T} ℃ R4 (a) Is S linearly independent? (b) If S is linearly independent, then extend S to a basis for R4. If S is linearly dependent, then extend a subset of S to a basis for R4.

Let S = {[0, 1, −1, 2]T, [1, 2, 3, 0]T} ℃ R4 (a) Is S linearly independent? (b) If S is linearly independent, then extend S to a basis for R4. If S is linearly dependent, then extend a subset of S to a basis for R4.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.6: The Algebra Of Matrices
Problem 13E
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4. Let S = {[0, 1, −1, 2]T, [1, 2, 3, 0]T} ≤ Rª (a) Is S linearly independent? (b) If S is linearly independent, then extend S to a basis for R4. If S is linearly dependent, then extend a subset of S to a basis for R4.
Transcribed Image Text:4. Let S = {[0, 1, −1, 2]T, [1, 2, 3, 0]T} ≤ Rª (a) Is S linearly independent? (b) If S is linearly independent, then extend S to a basis for R4. If S is linearly dependent, then extend a subset of S to a basis for R4.
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