A root of equation left| {,begin{array}{*{20}{c}}{3 - x}&{ - 6}&3{ - 6}&{3 - x}&33&a

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3 and 4 .Determinants and Matrices

easy

A root of the equation $\left| {\,\begin{array}{*{20}{c}}{3 - x}&{ - 6}&3\\{ - 6}&{3 - x}&3\\3&3&{ - 6 - x}\end{array}\,} \right| = 0$ is

A

$6$

B

$3$

C

$0$

D

None of these

Solution

(c) Applying ${C_1} \to {C_1} + {C_2} + {C_3}$, we obtain

$ – x\,\left| {\,\begin{array}{*{20}{c}}1&{ – 6}&3\\1&{3 – x}&3\\1&3&{ – 6 – x}\end{array}\,} \right|$ = 0

$ \Rightarrow $$ – x\,\left| {\,\begin{array}{*{20}{c}}1&{ – 6}&3\\0&{9 – x}&0\\0&9&{ – 9 – x}\end{array}\,} \right| = 0$

$ \Rightarrow $ $ – x(9 – x)\,( – 9 – x) = 0 \Rightarrow x = 0,\,9,\, – 9$.

Trick : Check by assuming the values of $x$ from the given options.

Standard 12

Mathematics

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