Compute the following determinant. vert } 3&-1 5&0 vert square square

To compute the determinant of the given 2x2 matrix, we can use the formula:<br /><br />$\text{det} \begin{pmatrix} a & b \\ c & d \end{pmatrix} = ad - bc$<br /><br />In this case, the matrix is:<br /><br />$\begin{pmatrix} 3 & -1 \\ 5 & 0 \end{pmatrix}$<br /><br />So, applying the formula:<br /><br />$\text{det} \begin{pmatrix} 3 & -1 \\ 5 & 0 \end{pmatrix} = (3)(0) - (-1)(5) = 0 + 5 = 5$<br /><br />Therefore, the determinant of the given matrix is 5.