Needed to be solved correctly in 30 minutes and get the thumbs up please show neat and clean work Question 2(a) Find an orthonormal basis of the vector space P₂ of polynomials of degreeat most 2 with respect to the inner product(f. g) = [°¸ ƒ(x)g(x) dxShow your working.(b) Let A be the following matrix:A =1 0 a0a 0 1For a 0, find an eigendecomposition of A.(c) Consider the set W of all 2 x 2 matrices A such that both (1, 2) and(2,-1) are eigenvectors of A. Prove that W is a subspace of the space ofall 2 x 2 matrices and find the dimension of W.

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Question 2 (a) Find an orthonormal basis of the vector space P₂ of polynomials of degree at most 2 with respect to the inner product (f, g) = [ f(x)g(x) dx Show your working. (b) Let A be the following matrix: A 10 a 010 a 01 For a 0, find an eigendecomposition of A. (c) Consider the set W of all 2 x 2 matrices A such that both (1, 2) and (2, -1) are eigenvectors of A. Prove that W is a subspace of the space of all 2 x 2 matrices and find the dimension of W.

Question 2 (a) Find an orthonormal basis of the vector space P₂ of polynomials of degree at most 2 with respect to the inner product (f, g) = [ f(x)g(x) dx Show your working. (b) Let A be the following matrix: A 10 a 010 a 01 For a 0, find an eigendecomposition of A. (c) Consider the set W of all 2 x 2 matrices A such that both (1, 2) and (2, -1) are eigenvectors of A. Prove that W is a subspace of the space of all 2 x 2 matrices and find the dimension of W.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices

Problem 29EQ

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