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STD 12 - 3 and 4 . determinant and metrices — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 3 and 4 . determinant and metrices1 Mark
MCQ
The value of the determinant $\left| {\,\begin{array}{*{20}{c}}1&1&1\\{b + c}&{c + a}&{a + b}\\{b + c - a}&{c + a - b}&{a + b - c}\end{array}\,} \right|$ is
  • A
    $abc$
  • B
    $a + b + c$
  • C
    $ab + bc + ca$
  • ✓
    $0$
✓

Answer

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

= $\left| {\,\begin{array}{*{20}{c}}0&0&1\\{b - a}&{c - b}&{a + b}\\{2\,(b - a)}&{2\,(c - b)}&{a + b - c}\end{array}\,} \right|\, = 0$.

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