Video: Evaluating a Determinant in Terms of π‘₯

Find the value of the determinant 𝐴 = [π‘₯, βˆ’11 and π‘₯, βˆ’1].

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Video Transcript

Find the value of the determinant of matrix 𝐴: π‘₯, negative 11, π‘₯, 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 π‘Ž, 𝑏, 𝑐, 𝑑 is equal to π‘Žπ‘‘ minus 𝑏𝑐. This means that the determinant of the matrix π‘₯, negative 11, π‘₯, negative one is equal to π‘₯ multiplied by negative one minus negative 11 multiplied by π‘₯. Multiplying the top-left and bottom-right value gives us negative π‘₯. Multiplying the top-right and bottom-left value gives us negative 11π‘₯. We need to subtract this from negative π‘₯. This can be simplified to negative π‘₯ plus 11π‘₯. The determinant of matrix 𝐴: π‘₯, negative 11, π‘₯, negative one is therefore equal to 10π‘₯.

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