Question

evaluate the determinant of the matrix. $\begin{bmatrix} 6&-3\\ -8&3end{bmatrix}$
the determinant is $square$

Explanation:

Step1: Recall 2x2 determinant formula

For matrix

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

, determinant is $ad - bc$.

Step2: Substitute values into formula

Here $a=6, b=-3, c=-8, d=3$.
$\text{Determinant} = (6)(3) - (-3)(-8)$

Step3: Calculate each product

$6\times3=18$, $(-3)\times(-8)=24$

Step4: Compute final result

$18 - 24 = -6$

Answer:

$-6$