Which of the following statements about matrices is not true? O Let A be an (n x n) matrix. If two of the rows of A are proportional, then |A| = 0. Suppose A is an (mxn) matrix and B is an (nxp) matrix. If AB = 0, this must mean that A = 0 or B = 0. 1 Any square matrix Anxn with a determinant |A| # 0 has a unique inverse A-1 given by A-1 = |A| O A necessary and sufficient condition for a square matrix Anxn to be nonsingular is |A| * 0. O None of the above O No answer adj (A)
Which of the following statements about matrices is not true? O Let A be an (n x n) matrix. If two of the rows of A are proportional, then |A| = 0. Suppose A is an (mxn) matrix and B is an (nxp) matrix. If AB = 0, this must mean that A = 0 or B = 0. 1 Any square matrix Anxn with a determinant |A| # 0 has a unique inverse A-1 given by A-1 = |A| O A necessary and sufficient condition for a square matrix Anxn to be nonsingular is |A| * 0. O None of the above O No answer adj (A)
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:Which of the following statements about matrices is not true?
Let A be an (nx n) matrix. If two of the rows of A are proportional, then |A| = 0.
Suppose A is an (mxn) matrix and B is an (n×p) matrix. If AB = 0, this must mean that A = 0 or B = 0.
1
Any square matrix Anxn with a determinant |A| # 0 has a unique inverse A-1 given by A -1 =
- adj (A)
|A|
A necessary and sufficient condition for a square matrix Anxn to be nonsingular is |A| # 0.
None of the above
No answer
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