Find the value of x that makes the matrix A singular A 5 2

Find the value of x that makes the matrix A singular: A = [5 -2 x -4]

Solution

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A square matrix is singular if and only if its determinant is 0.

det(A) = (5)(-4) - (-2)(x)

= -20 + 2x = 0

2x = 20

x = 10

=> For x = 10, matrix is singular.