or spaces (10 points) dimensional matrix A for which the determinant |A| < 0. Ment it is true or false. (correct answer = 1 point, wrong answer = -1 ple. equal to 0. A are linearly dependent. re linearly independent. re real-valued. ve definite. ite when N is even. tible. ogonal.
or spaces (10 points) dimensional matrix A for which the determinant |A| < 0. Ment it is true or false. (correct answer = 1 point, wrong answer = -1 ple. equal to 0. A are linearly dependent. re linearly independent. re real-valued. ve definite. ite when N is even. tible. ogonal.
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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Transcribed Image Text:Question 1: Matrices and vector spaces (10 points)
Consider the symmetric NxN-dimensional matrix A for which the determinant |A| < 0. Mention for each
of the following statements if it is true or false. (correct answer = 1 point, wrong answer = -1 point, no
answer = 0 points)
1. The matrix A is invertible.
2.
The null space of A is equal to 0.
3. The column vectors of A are linearly dependent.
4. The row vectors of A are linearly independent.
5. rank(A) < N
6. The eigenvalues of A are real-valued.
7. The matrix A is negative definite.
8.
The matrix A is indefinite when N is even.
9. The matrix ATA is invertible.
10. The matrix ATA is orthogonal.
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