'5. Consider the 5 × 5 symmetric matrix over R 10 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1. A = The rank is the number of linearly independent row (or column) vectors of A. (i) Find the rank of the matrix. Explain. (ii) Find the determinant and trace of the matrix. (iii) Find all eigenvalues of the matrix. (iv) Find one eigenvector. (v) Is the matrix positive semidefinite?
'5. Consider the 5 × 5 symmetric matrix over R 10 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1. A = The rank is the number of linearly independent row (or column) vectors of A. (i) Find the rank of the matrix. Explain. (ii) Find the determinant and trace of the matrix. (iii) Find all eigenvalues of the matrix. (iv) Find one eigenvector. (v) Is the matrix positive semidefinite?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 26EQ
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