(iv) If A is a symmetric matrix then x-Ax is a positive definite quadratic form. (v) If A is an n xn matrix then there is a basis of R" made up of orthogonal eigenvectors for A. (vi) Any spanning set of a vector space is a basis. (vii) The orthogonal complement of the columnspace of A is the rowspace of 4. (viii) If A is diagonalizable then A is invertible. Determine wlhich of the above statements are True (1) or False (2).

(iv) If A is a symmetric matrix then x-Ax is a positive definite quadratic form. (v) If A is an n xn matrix then there is a basis of R" made up of orthogonal eigenvectors for A. (vi) Any spanning set of a vector space is a basis. (vii) The orthogonal complement of the columnspace of A is the rowspace of 4. (viii) If A is diagonalizable then A is invertible. Determine wlhich of the above statements are True (1) or False (2).

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 27EQ

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