Video: Evaluating a Determinant in Terms of 𝑥

Video Transcript

Find the value of the determinant of matrix 𝐴: 𝑥, negative 11, 𝑥, negative one.

The determinant of a matrix is denoted by absolute value bars, and the determinant of any two-by-two matrix of the form 𝑎, 𝑏, 𝑐, 𝑑 is equal to 𝑎𝑑 minus 𝑏𝑐. This means that the determinant of the matrix 𝑥, negative 11, 𝑥, negative one is equal to 𝑥 multiplied by negative one minus negative 11 multiplied by 𝑥. Multiplying the top-left and bottom-right value gives us negative 𝑥. Multiplying the top-right and bottom-left value gives us negative 11𝑥. We need to subtract this from negative 𝑥. This can be simplified to negative 𝑥 plus 11𝑥. The determinant of matrix 𝐴: 𝑥, negative 11, 𝑥, negative one is therefore equal to 10𝑥.