Chapter 11, Problem 17CT

To determine

To calculate: The value of determinant $\left|\begin{array}{cc}-2& 5\\ 3& 7\end{array}\right|$.

Answer to Problem 17CT

Solution:

The value of the determinant $\left|\begin{array}{cc}-2& 5\\ 3& 7\end{array}\right|$ is $-29$.

Explanation of Solution

Given information:

The determinant, $\left|\begin{array}{cc}-2& 5\\ 3& 7\end{array}\right|$.

Formula used:

If $a,b,c,$ and $d$ are four real numbers, the symbol $D=\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|$ is called determinant and its value is the number $ad-bc$.

Calculation:

Compare the determinant $\left|\begin{array}{cc}-2& 5\\ 3& 7\end{array}\right|$ with $\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|$.

Here, $a=-2,b=5,c=3$, and $d=7$.

So, the value of determinant is $ad-bc=\left(-2\right)\left(7\right)-\left(5\right)\left(3\right)=-14-15=-29$.

Hence, the value of the determinant $\left|\begin{array}{cc}-2& 5\\ 3& 7\end{array}\right|$ is $-29$.