jee-advanced 2006 Q31

jee-advanced · India Matrices Linear System and Inverse Existence

31. The sum of the elements of $\mathrm { U } ^ { - 1 }$ is
(A) - 1
(B) 0
(C) 1
(D) 3
Sol. (B) Moreover adj $\mathrm { U } = \left[ \begin{array} { c c c } - 1 & - 2 & 0 \\ - 7 & - 5 & - 3 \\ 9 & 6 & 3 \end{array} \right]$. Hence $\mathrm { U } ^ { - 1 } = \frac { \operatorname { adj } \mathrm { U } } { 3 }$ and sum of the elements of $\mathrm { U } ^ { - 1 } = 0$.

The sum of the elements of $\mathrm { U } ^ { - 1 }$ is

31. The sum of the elements of $\mathrm { U } ^ { - 1 }$ is\\
(A) - 1\\
(B) 0\\
(C) 1\\
(D) 3

Sol. (B)\\
Moreover adj $\mathrm { U } = \left[ \begin{array} { c c c } - 1 & - 2 & 0 \\ - 7 & - 5 & - 3 \\ 9 & 6 & 3 \end{array} \right]$.\\
Hence $\mathrm { U } ^ { - 1 } = \frac { \operatorname { adj } \mathrm { U } } { 3 }$ and sum of the elements of $\mathrm { U } ^ { - 1 } = 0$.\\

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