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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}}1&1&1\\1&{1 + x}&1\\1&1&{1 + y}\end{array}\,} \right| = $
  • A
    $1$
  • B
    $0$
  • C
    $x$
  • ✓
    $xy$
✓

Answer

Correct option: D.
$xy$
d
(d) $\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&{1 + x}&1\\1&1&{1 + y}\end{array}\,} \right| = \left| {\,\begin{array}{*{20}{c}}0&0&1\\{ - x}&x&1\\0&{ - y}&{1 + y}\end{array}\,} \right| = xy,$

[${C_1} \to {C_1} - {C_2}$    ;  ${C_2} \to {C_2} - {C_3}$]

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