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Let's now consider W, the subspace of R5 having basis 14 V1 = 1 -6 8 2 Evaluate (Sage) " V2 = 10 -3 4 3 a. Apply the Gram-Schmidt algorithm to find an orthogonal basis w₁, W2, and W3 for W. b. Find 1, the orthogonal projection of b = V3 = -5 11 3 0 -2 0 onto W. -1 5 c. Explain why we know that is a linear combination of the original vectors V₁, V2, and v3 and then find weights so that 6 = C₁V₁ + C₂V₂ + C3V3.

Let's now consider W, the subspace of R5 having basis 14 V1 = 1 -6 8 2 Evaluate (Sage) " V2 = 10 -3 4 3 a. Apply the Gram-Schmidt algorithm to find an orthogonal basis w₁, W2, and W3 for W. b. Find 1, the orthogonal projection of b = V3 = -5 11 3 0 -2 0 onto W. -1 5 c. Explain why we know that is a linear combination of the original vectors V₁, V2, and v3 and then find weights so that 6 = C₁V₁ + C₂V₂ + C3V3.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 22EQ
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Subject: calculus 

 

Let's now consider W, the subspace of R5 having basis V1 = 1 14 -6 Evaluate (Sage) 8 2 V2 = -3 4 3 6= a. Apply the Gram-Schmidt algorithm to find an orthogonal basis w₁, W2, and W3 for W " b. Find 6, the orthogonal projection of b = V3 = 2 3 0 -2 11 -1 0 onto W. -1 5 c. Explain why we know that is a linear combination of the original vectors V₁, V2, and v3 and then find weights so that = C1V1 + C₂V2 + C3V3.
Transcribed Image Text:Let's now consider W, the subspace of R5 having basis V1 = 1 14 -6 Evaluate (Sage) 8 2 V2 = -3 4 3 6= a. Apply the Gram-Schmidt algorithm to find an orthogonal basis w₁, W2, and W3 for W " b. Find 6, the orthogonal projection of b = V3 = 2 3 0 -2 11 -1 0 onto W. -1 5 c. Explain why we know that is a linear combination of the original vectors V₁, V2, and v3 and then find weights so that = C1V1 + C₂V2 + C3V3.
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