Determinants

What is the value of the determinant \( \begin{vmatrix} 3 & 5 \\ 2 & 7 \end{vmatrix} \)?

If \( \begin{vmatrix} x & 2 \\ 3 & 4 \end{vmatrix} = 10 \), find the value of \(x\).

The determinant of \( \begin{vmatrix} 1 & 0 & 2 \\ -1 & 3 & 1 \\ 2 & 1 & 0 \end{vmatrix} \) is:

If \( \begin{vmatrix} a & b \\ c & d \end{vmatrix} = 0 \), then which of the following is true?

Find the determinant of \( \begin{vmatrix} 2 & 3 \\ 4 & k \end{vmatrix} \) if it equals zero.

Evaluate \( \begin{vmatrix} 1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0 \end{vmatrix} \).

If \( A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix} \), find \( \det(3A) \).

Which of the following properties is true for determinants?

If \( \begin{vmatrix} 1 & 2 & 3 \\ 0 & x & 4 \\ 5 & 6 & 0 \end{vmatrix} = 1 \), find \(x\).

If the determinant \( \begin{vmatrix} 2 & 3 & 1 \\ 4 & 1 & 5 \\ 3 & 2 & k \end{vmatrix} = 0 \), find \(k\).