The inverse of $\left[\begin{array}{ccc}1& 2& 3\\ 0& 1& 2\\ 0& 0& 1\end{array}\right]$ is -

Important Questions on Determinants

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>EXERCISE>Q 7

If $A$ and $B$ are non-singular square matrices of same order, then $adj\left(AB\right)$ is equal to -

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>EXERCISE>Q 8

If $I_3$ is the identity matrix of order $3,$ then $I_3^{-1}$ is -

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>EXERCISE>Q 9

Inverse of the matrix $\left[\begin{array}{c}\cos 2\mathrm{\theta } –\sin 2\mathrm{\theta }\\ \sin 2\mathrm{\theta } \cos 2\mathrm{\theta }\end{array}\right]\mathrm{i}\mathrm{s}$

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>EXERCISE>Q 10

$A=\left[\begin{array}{lll}1& 0& 0\\ 0& 1& 1\\ 0& -2& 4\end{array}\right], I=\left[\begin{array}{lll}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$,  $A^{-1}=\frac{1}{6}\left(A^2+cA+dI\right)$ where $c,d\in R,$ then pair of values $(c,d)$ is

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>EXERCISE>Q 11

$x+ky-z=0,3x-ky-z=0$ and $x-3y+z=0$ has non-zero solution for $k=$

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>EXERCISE>Q 12

If $a_{1}x+b_{1}y+c_{1}z=0, a_{2}x+b_{2}y+c_{2}z=0, a_{3}x+b_{3}y+c_{3}z=0$ and $\left|\begin{array}{ccc}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3\end{array}\right|=0$, then the given system has -

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>EXERCISE>Q 13

The existence of the unique solution of the system $x+y+z=\lambda , 5x-y+\mu z=10, 2x+3y-z=6$ depends -

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>EXERCISE>Q 14

The value of $\lambda$ for which the system of equations $2x-y-z=12, x-2y+z=-4, x+y+\lambda z=4$ has no solution is -