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3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
MCQ
The solution $(s)$ of the equation $\left| {\begin{array}{*{20}{c}}x&a&b\\ a&x&a\\b&b&x\end{array}} \right|$ $= 0$ is/are :
  • A
    $x = - (a + b)$
  • B
    $x = a$
  • C
    $x = b$
  • ✓
    All of the above
✓

Answer

Correct option: D.
All of the above
d
Use $c_1 \rightarrow c_1 -c_2$ and then $R_1 \rightarrow R_1 + R_2 $ to get $\left| {\,\begin{array}{*{20}{c}}0&{a + x}&{b + a}\\{ - (x - a)}&x&a\\0&b&x \end{array}\,} \right|$ $= 0$. Now open by $c_1$ and foctorize

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