Question

compute the following determinant.
\

$$\begin{vmatrix} 6 & 3 \\\\ -3 & 5 \\end{vmatrix}$$

Explanation:

Step1: Recall determinant formula for 2x2 matrix

For a matrix

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

, the determinant is $ad - bc$.

Step2: Substitute values into formula

Here, $a = 6$, $b = 3$, $c = -3$, $d = 5$. So determinant is $6\times5 - 3\times(-3)$.

Step3: Calculate each term

$6\times5 = 30$, $3\times(-3)= -9$. Then $30 - (-9)=30 + 9 = 39$.

Answer:

39