A matrix becomes singular when its determinant is equal to zero. The determinant of a 3x3 matrix [a b c; d e f; g h i] is calculated as follows:

det = aei + bfg + cdh - ceg - bdi - afh

For the given matrix, a=8, b=4, c=1, d=2, e=x, f=0, g=6, h=0, i=2. Substituting these values into the determinant formula gives:

det = 8*x*2 + 4*0*6 + 1*2*0 - 1*x*6 - 4*2*2 - 8*0*0

Simplifying this gives:

det = 16x - 6x - 16 = 10x - 16

Setting the determinant equal to zero gives the equation 10x - 16 = 0. Solving for x gives x = 16/10 = 1.6.

So, the matrix becomes singular when x = 1.6.

Question

A matrix becomes singular when its determinant is equal to zero. The determinant of a 3x3 matrix [a b c; d e f; g h i] is calculated as follows:

det = aei + bfg + cdh - ceg - bdi - afh

For the given matrix, a=8, b=4, c=1, d=2, e=x, f=0, g=6, h=0, i=2. Substituting these values into the determinant formula gives:

det = 8*x*2 + 4*0*6 + 1*2*0 - 1*x*6 - 4*2*2 - 8*0*0

Simplifying this gives:

det = 16x - 6x - 16 = 10x - 16

Setting the determinant equal to zero gives the equation 10x - 16 = 0. Solving for x gives x = 16/10 = 1.6.

So, the matrix becomes singular when x = 1.6.

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