MCQ
Let $A =$ $\left[ {\begin{array}{*{20}{c}}{x + \lambda }&x&x\\x&{x + \lambda}&x\\x&x&{x + \lambda }\end{array}} \right]$ , then $A^{-1}$ exists if
- A$x \ne 0$
- B$\lambda \ne 0$
- ✓$3x + \lambda \ne 0, \lambda \ne 0$
- D$x \ne 0, \lambda \ne 0$
$=$ $(3x + \lambda )$ $\left[{\begin{array}{*{20}{c}}1&x&x\\0&\lambda &0\\0&0&\lambda \end{array}} \right]$ $= \lambda ^2(3x + \lambda )$ [Take $3x + \lambda$ common and use $R_2 \rightarrow R_2 -R_1, R_3 \rightarrow R_3- R_1$]
Thus, $A^{-1}$ will exist if $\lambda \ne 0$ and $3x + \lambda \ne 0$
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