Consider the vectors a₁ = (-1, 2, 2), a2 = (2,2, -1), and a3 = (2, -1,2).1. Compute the projection matrices P₁ and P2 onto the lines in the direction of a₁ and a2, respectively. Multiplythose projection matrices and explain why their product is what it is.2. Find the projection vectors P1, P2, and p3 of 6 = (1,0,0) onto the lines in the direction of a1, a2, and ã3. Addthe three projections p₁ + √2 + 3. What do you notice? Why does this make sense?3. Find the projection matrix P3 onto the line directed by ã3, then find P₁ + P2 + P3. Comment on the result(explain why it makes sense).

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Consider the vectors ā₁ = (-1,2,2), a2 = (2,2, -1), and 3 = (2,-1,2). 1. Compute the projection matrices P₁ and P2 onto the lines in the direction of a₁ and a2, respectively. Multiply those projection matrices and explain why their product is what it is. 2. Find the projection vectors P1, P2, and 3 of 6 = (1,0,0) onto the lines in the direction of a1, a2, and 3. Add the three projections p₁ + 2 + 3. What do you notice? Why does this make sense? 3. Find the projection matrix P3 onto the line directed by aз, then find P₁ + P2 P3. Comment on the result (explain why it makes sense).

Consider the vectors ā₁ = (-1,2,2), a2 = (2,2, -1), and 3 = (2,-1,2). 1. Compute the projection matrices P₁ and P2 onto the lines in the direction of a₁ and a2, respectively. Multiply those projection matrices and explain why their product is what it is. 2. Find the projection vectors P1, P2, and 3 of 6 = (1,0,0) onto the lines in the direction of a1, a2, and 3. Add the three projections p₁ + 2 + 3. What do you notice? Why does this make sense? 3. Find the projection matrix P3 onto the line directed by aз, then find P₁ + P2 P3. Comment on the result (explain why it makes sense).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.3: Lines And Planes

Problem 18EQ

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