Suppose a vector w R³ can be written as w = 5v₁ - 3v2 + 7v3, where V₁, V2, V3 are vectors in R³. Which of the following statements must be true? Statement 1: Every vector in R³ can be written as a linear combination of V₁, V2, V3. Statement 2: V2 is a linear combination of w, V₁, V3. Select one alternative: Statement 1 is true, and Statement 2 is true Statement 1 is false, and Statement 2 is false Statement 1 is true, and Statement 2 is false Statement 1 is false, and Statement 2 is true
Suppose a vector w R³ can be written as w = 5v₁ - 3v2 + 7v3, where V₁, V2, V3 are vectors in R³. Which of the following statements must be true? Statement 1: Every vector in R³ can be written as a linear combination of V₁, V2, V3. Statement 2: V2 is a linear combination of w, V₁, V3. Select one alternative: Statement 1 is true, and Statement 2 is true Statement 1 is false, and Statement 2 is false Statement 1 is true, and Statement 2 is false Statement 1 is false, and Statement 2 is true
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.2: Length And Angle: The Dot Product
Problem 17EQ
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