In Exercises 7779, a property of determinants is given (A and B are square matrices)
Chapter 8, Problem 77(choose chapter or problem)
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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