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)

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter11: Matrices And Determinants

Section11.CR: Chapter Review

Problem 11CC

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Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and nullity of AB. b Show that matrices A and B must be identical.
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11. Find two nonzero matrices and such that.

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