Chapter A, Problem 1E

To determine

To calculate: The value of the determinant, $\left|\begin{array}{cc}5& 6\\ 2& 1\end{array}\right|$.

Answer to Problem 1E

Solution:

The value of the determinant $\left|\begin{array}{cc}5& 6\\ 2& 1\end{array}\right|$ is $\underset{\_}{-7}$.

Explanation of Solution

Given:

The determinant is $\left|\begin{array}{cc}5& 6\\ 2& 1\end{array}\right|$.

Formula used:

The magnitude of second order determinant $\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|$ is,

$ad-cb$.

Calculation:

Consider the determinant,

$\left|\begin{array}{cc}5& 6\\ 2& 1\end{array}\right|$.

Recall the formula for value of determinant,

$ad-cb$

Substitute 5 for a, 6 for b, 2 for c, and 1 for d,

$\begin{array}{ccc}\hfill \left|\begin{array}{cc}\hfill 5& 6\\ \hfill 2& 1\end{array}\right|& =& \left(5\right)\left(1\right)-\left(6\right)\left(2\right)\hfill \\ \hfill & =& 5-12\hfill \\ \hfill & =& -7\hfill \end{array}$

The value of the determinant is $-7$.