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3 and 4 .Determinants and Matrices
easy
$\left| {\,\begin{array}{*{20}{c}}1&a&b\\{ - a}&1&c\\{ - b}&{ - c}&1\end{array}\,} \right| = $
A
$1 + {a^2} + {b^2} + {c^2}$
B
$1 - {a^2} + {b^2} + {c^2}$
C
$1 + {a^2} + {b^2} - {c^2}$
D
$1 + {a^2} - {b^2} + {c^2}$
Solution
(a) $\left| {\,\begin{array}{*{20}{c}}1&a&b\\{ – a}&1&c\\{ – b}&{ – c}&1\end{array}\,} \right| = 1\,(1 + {c^2}) – a( – a + bc) + b(ac + b)$
= $1 + {a^2} + {b^2} + {c^2}$.
Standard 12
Mathematics