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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
$\left| {\,\begin{array}{*{20}{c}}{{b^2} - ab}&{b - c}&{bc - ac}\\{ab - {a^2}}&{a - b}&{{b^2} - ab}\\{bc - ac}&{c - a}&{ab - {a^2}}\end{array}\,} \right| = $
  • A
    $abc(a + b + c)$
  • B
    $3{a^2}{b^2}{c^2}$
  • ✓
    $0$
  • D
    None of these
✓

Answer

Correct option: C.
$0$
c
(c) $\Delta = (b - a)\,(b - a)\,.\,\left| {\,\begin{array}{*{20}{c}}b&{b - c}&c\\a&{a - b}&b\\c&{c - a}&a\end{array}\,} \right|$

= ${(a - b)^2}\left| {\,\begin{array}{*{20}{c}}b&b&c\\a&a&b\\c&c&a\end{array}\,} \right|\, = 0$, [by ${C_2} \to {C_2} + {C_3}$] .

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