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3 and 4 .Determinants and Matrices
normal
If system of equations $kx + 2y - z = 2,$$\left( {k - 1} \right)x + ky + z = 1,x + \left( {k - 1} \right)y + kz = 3$ has only one solution, then number of possible real value$(s)$ of $k$ is -
A
$0$
B
$1$
C
$2$
D
infinite
Solution
$\left|\begin{array}{ccc}{k} & {2} & {-1} \\ {(k-1)} & {k} & {1} \\ {1} & {(k-1)} & {k}\end{array}\right| \neq 0$
$\Rightarrow \mathrm{k}$ has infinite solutions
Standard 12
Mathematics