Chapter C.2, Problem 1E

To determine

To evaluate: The value of $\left|\begin{array}{cc}3& 4\\ -2& 1\end{array}\right|$.

Answer to Problem 1E

The value of the determinant is $\underset{\_}{\text{11}}$.

Explanation of Solution

Procedure used:

Steps for evaluating a $\text{2}\times \text{2}$ determinant:

“1. Find the product of the elements on the diagonal including the first element of the first column.

2. Find the product of the elements on the diagonal including the second element of the first column.

3. Subtract the products found in Step 1 and Step 2.”

Calculation:

The given determinant is $\left|\begin{array}{cc}3& 4\\ -2& 1\end{array}\right|$.

Evaluate the determinant as follows.

$\begin{array}{c}\left|\begin{array}{cc}3& 4\\ -2& 1\end{array}\right|=3\left(1\right)-4\left(-2\right)\\ =3+8\\ =11\end{array}$

Thus, the value of the determinant is $\underset{\_}{\text{11}}$.