Question

PROPERTIES OF DETERMINANTS In Exercises 97-99, 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 or interchanging two columns of $A$, then $|B| = -|A|$. (a) $\left| \begin{array}{r} 1 && 3 & 4 \\ -7 && 2 & -5 \\ 6 && 1 & 2 \end{array} \right| = -\left| \begin{array}{r} 1 & 4 && 3 \\ -7 & -5 && 2 \\ 6 & 2 && 1 \end{array} \right|$ (b) $\left| \begin{array}{r} 1 && 3 && 4 \\ -2 && 2 && 0 \\ 1 && 6 && 2 \end{array} \right| = -\left| \begin{array}{r} 1 && 6 && 2 \\ -2 && 2 && 0 \\ 1 && 3 && 4 \end{array} \right|$

Name: Problem 97, Chapter 8: Precalculus with Limits
Uploaded: 2020-01-07T01:52:23-08:00
Duration: 2 min 28 s
Channel: Foster Wisusik

   PROPERTIES OF DETERMINANTS In Exercises 97-99, 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 or interchanging two columns of $A$, then $|B| = -|A|$.

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

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

Precalculus with Limits

Ron Larson 2nd Edition

Chapter 8, Problem 97

Instant Answer

Solved by Expert Foster Wisusik

01/07/2020

Step 1

The property states that if we interchange two rows or two columns in a matrix $A$ to obtain a new matrix $B$, then the determinant of $B$ is the negative of the determinant of $A$. This is represented as $|B| = -|A|$. Show more…

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PROPERTIES OF DETERMINANTS In Exercises 97-99, 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 or interchanging two columns of $A$, then $|B| = -|A|$. (a) $\left| \begin{array}{r} 1 && 3 & 4 \\ -7 && 2 & -5 \\ 6 && 1 & 2 \end{array} \right| = -\left| \begin{array}{r} 1 & 4 && 3 \\ -7 & -5 && 2 \\ 6 & 2 && 1 \end{array} \right|$ (b) $\left| \begin{array}{r} 1 && 3 && 4 \\ -2 && 2 && 0 \\ 1 && 6 && 2 \end{array} \right| = -\left| \begin{array}{r} 1 && 6 && 2 \\ -2 && 2 && 0 \\ 1 && 3 && 4 \end{array} \right|$