In Exercises 7779, a property of determinants is given (A and B are square matrices)

Chapter 8, Problem 77

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Properties of Determinants In Exercises 77-79, a property of determinants is given (A and B are square matrices). State how the property has been applied to the given determinants and use a graphing utility to verify the results.

If B is obtained from A by interchanging two rows of A or by interchanging two columns of A, then |B|  = − |A|.

(a) \(\left|\begin{array}{rrr} 1 & 3 & 4 \\ -7 & 2 & -5 \\ 6 & 1 & 2 \end{array}\right|=-\left|\begin{array}{rrr} 1 & 4 & 3 \\ -7 & -5 & 2 \\ 6 & 2 & 1 \end{array}\right|\)

(b) \(\left|\begin{array}{rrr} 1 & 3 & 4 \\ -2 & 2 & 0 \\ 1 & 6 & 2 \end{array}\right|=-\left|\begin{array}{rrr} 1 & 6 & 2 \\ -2 & 2 & 0 \\ 1 & 3 & 4 \end{array}\right|\)

Text Transcription:

|_6  1  2  ^-7  2  -5  ^^1  3  4| = - |_6  2  1  ^-7  -5  2  ^^1  4  3|

|_1  6  2  ^-2  2  0  ^^1  3  4| = - |_1  3  4  ^-2  2  0  ^^1  6  2|

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