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(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).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Only answer the last four please
(iv) If A is a symmetric matrix then x Ax is a positive definite quadratic form. (v) If A is an n ×n 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 which of the above statements are True (1) or False (2).
Transcribed Image Text:(iv) If A is a symmetric matrix then x Ax is a positive definite quadratic form. (v) If A is an n ×n 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 which of the above statements are True (1) or False (2).
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