Consider the following set of vectors. V₁ = V₂ = V3 = Consider the following equation. Let V₁, V₂, and v3 be (column) vectors in R3 and let A be the 3 x 3 matrix [V₁ V₁ V₂ V3 with these vectors as its columns. Then V₁, V₂, and v3 are linearly dependent if and only if the homogeneous linear system with augmented matrix [A10] has a nontrivi solution. 0 -8-8-8-8 C1 + C3 0 = 0 0 Solve for C₁, C₂, and C3. If a nontrivial solution exists, state it or state the general solution in terms of the parameter t. (If only the trivial solution exists, enter the trivial solution {C₁, C₂, C3} = {0, 0, 0}.) {C₁, C₂, C3} = Determine if the vectors V₁, V₂, and v3 are linearly independent. The set of vectors is linearly dependent. The set of vectors is linearly independent.
Consider the following set of vectors. V₁ = V₂ = V3 = Consider the following equation. Let V₁, V₂, and v3 be (column) vectors in R3 and let A be the 3 x 3 matrix [V₁ V₁ V₂ V3 with these vectors as its columns. Then V₁, V₂, and v3 are linearly dependent if and only if the homogeneous linear system with augmented matrix [A10] has a nontrivi solution. 0 -8-8-8-8 C1 + C3 0 = 0 0 Solve for C₁, C₂, and C3. If a nontrivial solution exists, state it or state the general solution in terms of the parameter t. (If only the trivial solution exists, enter the trivial solution {C₁, C₂, C3} = {0, 0, 0}.) {C₁, C₂, C3} = Determine if the vectors V₁, V₂, and v3 are linearly independent. The set of vectors is linearly dependent. The set of vectors is linearly independent.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 50EQ
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