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Negative marking applies. Consider the linear operator Pin a 3 dimensional linear vector space with basis functions (). P has the following action on the basis function: Pê, ê. Pêsê, and Pe Which of the following is the matrix from of P? OP OP OP [010] 001 00 0 100 Loo 10 01 0 0 100 Now select which of the following statements must be true: OP-I, where I is the identity matrix. OP³ès-é OP³ės - ēs. ²ė, -és □p³ès - Pès-és- OP³ė, -és- ope - I, where I is the identity matrix and is a positive integer. Op³ - I, where I is the identity matrix. OP'è - I, where I is the identity matrix and is a positive integer.

Negative marking applies. Consider the linear operator Pin a 3 dimensional linear vector space with basis functions (). P has the following action on the basis function: Pê, ê. Pêsê, and Pe Which of the following is the matrix from of P? OP OP OP [010] 001 00 0 100 Loo 10 01 0 0 100 Now select which of the following statements must be true: OP-I, where I is the identity matrix. OP³ès-é OP³ės - ēs. ²ė, -és □p³ès - Pès-és- OP³ė, -és- ope - I, where I is the identity matrix and is a positive integer. Op³ - I, where I is the identity matrix. OP'è - I, where I is the identity matrix and is a positive integer.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section: Chapter Questions
Problem 1RQ
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Consider the linear operator P^P^ in a 3 dimensional linear vector space with basis functions {e^i}{e^i}. P^P^ has the following action on the basis function: P^e^1=e^3P^e^1=e^3, P^e^2=e^1P^e^2=e^1, and P^e^3=e^2P^e^3=e^2.
Which of the following is the matrix from of P^P^?

Negative marking applies. Consider the linear operator Pin a 3 dimensional linear vector space with basis functions (). P has the following action on the basis function: Pê, ê. Pêsê, and Pe Which of the following is the matrix from of P? OP OP OP [010] 001 00 0 100 Loo 10 01 0 0 100 Now select which of the following statements must be true: OP-I, where I is the identity matrix. OP³ès-é OP³ės - ēs. ²ė, -és □p³ès - Pès-és- OP³ė, -és- ope - I, where I is the identity matrix and is a positive integer. Op³ - I, where I is the identity matrix. OP'è - I, where I is the identity matrix and is a positive integer.
Transcribed Image Text:Negative marking applies. Consider the linear operator Pin a 3 dimensional linear vector space with basis functions (). P has the following action on the basis function: Pê, ê. Pêsê, and Pe Which of the following is the matrix from of P? OP OP OP [010] 001 00 0 100 Loo 10 01 0 0 100 Now select which of the following statements must be true: OP-I, where I is the identity matrix. OP³ès-é OP³ės - ēs. ²ė, -és □p³ès - Pès-és- OP³ė, -és- ope - I, where I is the identity matrix and is a positive integer. Op³ - I, where I is the identity matrix. OP'è - I, where I is the identity matrix and is a positive integer.
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Once you do Pe1 = 0•e1 + 0•e2 + 1•e3 and then the same for Pe2 and Pe3, how do you know the matrix is 

0 1 0

0 0 1

1 0 0 

 

thank you :) 

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