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5 6 7 Compute the projection matrices aa/aa onto the lines through a₁ = (-1,2,2) and a2 =(2,2,-1). Multiply those projection matrices and explain why their prod- uct P₁P2 is what it is. Project b = (1,0,0) onto the lines through a₁ and a₂ in Problem 5 and also onto a3 (2,-1,2). Add up the three projections P₁ + P2+P3. Continuing Problems 5-6, find the projection matrix P3 onto a3 = (2,-1,2). Verify that P₁ + P₂+ P3 = I. This is because the basis a1, a2, a3 is orthogonal! a3 = W a₁ = a2 = 2 22 Questions 5-6-7: orthogonal a2 = a₁ = P1 P2a1 Questions 8-9-10: not orthogonal

5 6 7 Compute the projection matrices aa/aa onto the lines through a₁ = (-1,2,2) and a2 =(2,2,-1). Multiply those projection matrices and explain why their prod- uct P₁P2 is what it is. Project b = (1,0,0) onto the lines through a₁ and a₂ in Problem 5 and also onto a3 (2,-1,2). Add up the three projections P₁ + P2+P3. Continuing Problems 5-6, find the projection matrix P3 onto a3 = (2,-1,2). Verify that P₁ + P₂+ P3 = I. This is because the basis a1, a2, a3 is orthogonal! a3 = W a₁ = a2 = 2 22 Questions 5-6-7: orthogonal a2 = a₁ = P1 P2a1 Questions 8-9-10: not orthogonal

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I need help with question 7 please but it is related to question 5 and 6

5 6 7 Compute the projection matrices aa/aa onto the lines through a₁ = (-1,2,2) and a2 =(2,2,-1). Multiply those projection matrices and explain why their prod- uct P₁P2 is what it is. Project b = (1,0,0) onto the lines through a₁ and a₂ in Problem 5 and also onto a3 (2,-1,2). Add up the three projections P₁ + P2+P3. Continuing Problems 5-6, find the projection matrix P3 onto a3 = (2,-1,2). Verify that P₁ + P₂+ P3 = I. This is because the basis a1, a2, a3 is orthogonal! a3 = W a₁ = a2 = 2 22 Questions 5-6-7: orthogonal a2 = a₁ = P1 P2a1 Questions 8-9-10: not orthogonal
Transcribed Image Text:5 6 7 Compute the projection matrices aa/aa onto the lines through a₁ = (-1,2,2) and a2 =(2,2,-1). Multiply those projection matrices and explain why their prod- uct P₁P2 is what it is. Project b = (1,0,0) onto the lines through a₁ and a₂ in Problem 5 and also onto a3 (2,-1,2). Add up the three projections P₁ + P2+P3. Continuing Problems 5-6, find the projection matrix P3 onto a3 = (2,-1,2). Verify that P₁ + P₂+ P3 = I. This is because the basis a1, a2, a3 is orthogonal! a3 = W a₁ = a2 = 2 22 Questions 5-6-7: orthogonal a2 = a₁ = P1 P2a1 Questions 8-9-10: not orthogonal
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