Problem #2: Consider the following matrix A and column vectors K₁, K2, and K3. [5 6 6 6 5 6 6 6 5 A = 3 ··----0 4 K₂ = -4 K3 = 1 K₁ = -5 Verify that K₁, K2, and K3, are eigenvectors of the matrix A, and find the corresponding eigenvalues. Then use these eigenvectors, in the given order, along with the Gram-Schmidt process (where needed) to construct an orthogonal matrix P from these eigenvectors. (a) Enter the eigenvalues corresponding to K₁, K2, and K3 (in that order) into the answer box below, separated by commas. (b) Enter the values in the first row of the matrix P into the answer box below, separated by commas.

Problem #2: Consider the following matrix A and column vectors K₁, K2, and K3. [5 6 6 6 5 6 6 6 5 A = 3 ··----0 4 K₂ = -4 K3 = 1 K₁ = -5 Verify that K₁, K2, and K3, are eigenvectors of the matrix A, and find the corresponding eigenvalues. Then use these eigenvectors, in the given order, along with the Gram-Schmidt process (where needed) to construct an orthogonal matrix P from these eigenvectors. (a) Enter the eigenvalues corresponding to K₁, K2, and K3 (in that order) into the answer box below, separated by commas. (b) Enter the values in the first row of the matrix P into the answer box below, separated by commas.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.3: The Gram-schmidt Process And The Qr Factorization

Problem 8BEXP

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