Explanation The given statement is “If A has a row of zeros, then so does a d j ( A ) ” is false. Consider the matrix A = [ 1 2 0 0 ] . Now, calculate the cofactors of the matrix A as follows. C 11 = ( − 1 ) 1 + 1 ⋅ | 1 2 0 0 | ( Eliminate first row and first column ) = 0 Similarly, calculate the value of C 12 as shown below. C 12 = ( − 1 ) 1 + 2 ⋅ | 1 2 0 0 | ( Eliminate first row and second column ) = 0 Now, obtain the value of C 21 as follows

Elementary Linear Algebra: Applications Version

12th Edition

ISBN: 9781119282365

Author: Howard Anton, Chris Rorres, Anton Kaul

Publisher: WILEY

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Chapter 2.3, Problem 12TF

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Whether the statement “If A has a row of zeros, then so does adj(A) ” is true or false.

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Chapter 2.3, Problem 11TF

Chapter 2.3, Problem 1WT

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Elementary Linear Algebra: Applications Version

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Whether the statement “If A has a row of zeros, then so does a d j ( A ) ” is true or false.

Solution Summary: The author analyzes whether the statement "If A has a row of zeros, then so does adj(A)" is true or false.

Whether the statement “If A has a row of zeros, then so does adj(A) ” is true or false.

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Chapter 2 Solutions