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.