Chapter C, Problem 1VRC

To determine

The value of given determinant.

Answer to Problem 1VRC

Solution:

The value of given determinant $\left|\begin{array}{cc}7& 2\\ 0& 8\end{array}\right|$ is $56$.

Explanation of Solution

Concept:

Determinant of a $2\times 2$ matrix is given by,

$\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|=ad-bc$

Given:

The given matrix is $\left|\begin{array}{cc}7& 2\\ 0& 8\end{array}\right|$

Calculation:

Observe the given matrix and identify the values of $a,b,c$ and $d$.

$\left|\begin{array}{cc}7& 2\\ 0& 8\end{array}\right|$

From the matrix value of $a,b,c$ and $d$ are $7,2,0$ and $8$ respectively,

Substitute 7 for a, 2 for b, 0 for c and 8 for d in the formula to evaluate the determinant,

$\begin{array}{c}\left|\begin{array}{cc}7& 2\\ 0& 8\end{array}\right|=\left(7\times 8-2\times 0\right)\\ =56-0\\ =56\end{array}$

Final Statement:

Thus, the value of given determinant $\left|\begin{array}{cc}7& 2\\ 0& 8\end{array}\right|$ is $56$.