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
icon
Related questions
Question
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
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
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,