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Consider the symmetric NxN-dimensional matrix A for which the determinant |A| = 0, which of the following statements are true? 1. The matrix A is invertible. 2. The row vectors of A are linearly independent. 3. The column vectors of A are linearly dependent. 4. The null space of A is equal to 0. 5. rank(A)

Consider the symmetric NxN-dimensional matrix A for which the determinant |A| = 0, which of the following statements are true? 1. The matrix A is invertible. 2. The row vectors of A are linearly independent. 3. The column vectors of A are linearly dependent. 4. The null space of A is equal to 0. 5. rank(A)

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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Consider the symmetric NxN-dimensional matrix A for which the determinant |A| = 0, which of the following statements are true? 1. The matrix A is invertible. 2. The row vectors of A are linearly independent. 3. The column vectors of A are linearly dependent. 4. The null space of A is equal to 0. 5. rank(A) <N 6. The matrix AA is symmetric. 7. The matrix A is negative semi-definite. 8. All eigenvalues of A are real-valued. 9. At least one eigenvalue of A is equal to zero. 10. Exactly one eigenvalue of A is equal to zero.
Transcribed Image Text:Consider the symmetric NxN-dimensional matrix A for which the determinant |A| = 0, which of the following statements are true? 1. The matrix A is invertible. 2. The row vectors of A are linearly independent. 3. The column vectors of A are linearly dependent. 4. The null space of A is equal to 0. 5. rank(A) <N 6. The matrix AA is symmetric. 7. The matrix A is negative semi-definite. 8. All eigenvalues of A are real-valued. 9. At least one eigenvalue of A is equal to zero. 10. Exactly one eigenvalue of A is equal to zero.
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