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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 cofactor of the element $'4'$ in the determinant $\left| {\,\begin{array}{*{20}{c}}1&3&5&1\\2&3&4&2\\8&0&1&1\\0&2&1&1\end{array}\,} \right|$ is
  • A
    $4$
  • ✓
    $10$
  • C
    $-10$
  • D
    $-4$
✓

Answer

Correct option: B.
$10$
b
(b) The cofactor of element $4$, in the $2^{nd}$ row and ${3^{rd}}$ column is
$ = {( - 1)^{2 + 3}}\left| {\begin{array}{*{20}{c}}1&3&1\\8&0&1\\0&2&1\end{array}} \right|$

$=-{1(-2) -3 (8 -0)+ 1.16}= 10.$

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