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V₁ = [1 0 0]T, V₂ = [1 1 0]T v³ = [1 1 1]¹, and v₁ = [2_3_4]¹. V2 V3 a). Show that vi, i = 1,2,3 are linearly independent. b). Show that vi, i = 1, 2, 3, 4 are linearly dependent.

V₁ = [1 0 0]T, V₂ = [1 1 0]T v³ = [1 1 1]¹, and v₁ = [2_3_4]¹. V2 V3 a). Show that vi, i = 1,2,3 are linearly independent. b). Show that vi, i = 1, 2, 3, 4 are linearly dependent.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.1: The Geometry And Algebra Of Vectors
Problem 4EQ
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2. Consider the vectors: V₁ = [1 0 0]T, V₂ = [1 1 0]ª v³ = [1 1 1]ª, and v₁ = [2 3 4]. V3 a). Show that vi, i = 1,2,3 are linearly independent. b). Show that vi, i = 1, 2, 3, 4 are linearly dependent. c). Compute and compare v4TV4 and V4V4T.
Transcribed Image Text:2. Consider the vectors: V₁ = [1 0 0]T, V₂ = [1 1 0]ª v³ = [1 1 1]ª, and v₁ = [2 3 4]. V3 a). Show that vi, i = 1,2,3 are linearly independent. b). Show that vi, i = 1, 2, 3, 4 are linearly dependent. c). Compute and compare v4TV4 and V4V4T.
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