(C) matrix has no inverse if its determinant is $0$.Let $A = \begin{bmatrix} 1 & 3 & 2 \\ 2 & 5 & t \\ 4 & 7 - t & -6 \end{bmatrix}$.Setting $|A| = 0$

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(C) matrix has no inverse if its determinant is $0$.Let $A = \begin{bmatrix} 1 & 3 & 2 \\ 2 & 5 & t \\ 4 & 7 - t & -6 \end{bmatrix}$.Setting $|A| = 0$:$|A| = 1[5(-6) - t(7 - t)] - 3[2(-6) - 4t] + 2[2(7 - t) - 4(5)] = 0$$|A| = 1[-30 - 7t + t^2] - 3[-12 - 4t] + 2[14 - 2t - 20] = 0$$|A| = t^2 - 7t - 30 + 36 + 12t + 28 - 4t - 40 = 0$$|A| = t^2 + t - 6 = 0$Factoring the quadratic equation:$(t + 3)(t - 2) = 0$Thus,$t = -3$ or $t = 2$.

Class 12 Mathematics 3 and 4 .Determinants and Matrices Adjoint and inverse of matrices

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The values of $t$ such that the matrix $\begin{bmatrix} 1 & 3 & 2 \\ 2 & 5 & t \\ 4 & 7 - t & -6 \end{bmatrix}$ has no inverse,are

AP EAMCET 2018 All AP EAMCET

A
$3, 2$
B
$3, -2$
C
$-3, 2$
D
$-3, -2$

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3 and 4 .Determinants and Matrices

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Adjoint and inverse of matrices

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