| , * 20 c 1&a&b - a &1&c - b & - c &1 , | = - Vidyadip

MCQ

$\left| {\,\begin{array}{*{20}{c}}1&a&b\\{ - a}&1&c\\{ - b}&{ - c}&1\end{array}\,} \right| = $

✓
$1 + {a^2} + {b^2} + {c^2}$
B
$1 - {a^2} + {b^2} + {c^2}$
C
$1 + {a^2} + {b^2} - {c^2}$
D
$1 + {a^2} - {b^2} + {c^2}$

✓

Answer

Correct option: A.

$1 + {a^2} + {b^2} + {c^2}$

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

= $1 + {a^2} + {b^2} + {c^2}$.

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