Left| {,begin{array}{*{20}{c}}1&a&b{ - a}&1&c{ - b}&{ - c}&1end{array},} rig

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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

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