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3 and 4 .Determinants and Matrices
normal
If $n$ be the number of values of $x$ for which
matrix $\Delta (x) =\left[ {\begin{array}{*{20}{c}}
{ - x}&x&2\\
2&x&{ - x}\\
x&{ - 2}&{ - x}
\end{array}} \right]$ will be singular, then $det(\Delta\,(n))$ is
$($ where $det(B)$ denotes determinant of Matrix $B) -$
A
$-8$
B
$-6$
C
$0$
D
$10$
Solution
$\left|\begin{array}{ccc}{-x} & {x} & {2} \\ {2} & {x} & {-x} \\ {x} & {-2} & {-x}\end{array}\right|=0 \Rightarrow x=2,-2$
$\Rightarrow \quad n=2 \quad \Rightarrow \quad \Delta(n)=0$
Standard 12
Mathematics
