Question

evaluate the determinant.
$\

$$\begin{vmatrix}3&-6\\\\4&2\\end{vmatrix}$$

$
the answer is $\square$. (simplify your answer, if necessary.)

Explanation:

Step1: Apply 2x2 determinant formula

For

$$\begin{vmatrix} a & b \\ c & d \end{vmatrix}$$

, determinant = $ad - bc$.
Here, $a=3$, $b=-6$, $c=4$, $d=2$.
Expression: $3\times2 - (-6)\times4$

Step2: Calculate each product

Compute the two multiplication terms.
Expression: $6 - (-24)$

Step3: Simplify the expression

Resolve the subtraction of a negative number.
Expression: $6 + 24$

Step4: Sum the values

Add the remaining terms.
Expression: $30$

Answer:

30