AP EAMCET201825 Apr 2018Morning ShiftMathematicsMatricesActual

The values of t such that the matrix 1 3 2 2 5 t 4 7 - t - 6 has no inverse, are

Options

A3 , 2
B3 , - 2
C- 3 , 2
D- 3 , - 2

Correct answer

C. - 3 , 2

Step-by-step solution

Inverse of a matrix does not exist when the determinant of the matrix is zero. 1 3 2 2 5 t 4 7 - t - 6 = 0 ⇒ 1 - 30 - 7 t + t 2 - 3 - 12 - 4 t + 2 14 - 2 t - 20 = 0 ⇒ - 30 - 7 t + t 2 + 36 + 12 t - 12 - 4 t = 0 ⇒ t 2 + t - 6 = 0 ⇒ t 2 + 3 t - 2 t - 6 = 0 ⇒ t + 3 t - 2 = 0 ⇒ t = - 3   and   2 .

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