Left| {,begin{array}{*{20}{c}}{1/a}&{{a^2}}&{bc}{1/b}&{{b^2}}&{ca}{1/c}&{{c^2}}&

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3 and 4 .Determinants and Matrices

easy

$\left| {\,\begin{array}{*{20}{c}}{1/a}&{{a^2}}&{bc}\\{1/b}&{{b^2}}&{ca}\\{1/c}&{{c^2}}&{ab}\end{array}\,} \right| = $

A

$abc$

B

$1/abc$

C

$ab + bc + ca$

D

$0$

Solution

(d)$\left| {\,\begin{array}{*{20}{c}}{1/a}&{{a^2}}&{bc}\\{1/b}&{{b^2}}&{ca}\\{1/c}&{{c^2}}&{ab}\end{array}\,} \right|$$ = \frac{1}{{abc}}\,\left| {\,\begin{array}{*{20}{c}}1&{{a^3}}&{abc}\\1&{{b^3}}&{abc}\\1&{{c^3}}&{abc}\end{array}\,} \right| = \frac{{abc}}{{abc}}\left| {\,\begin{array}{*{20}{c}}1&{{a^3}}&1\\1&{{b^3}}&1\\1&{{c^3}}&1\end{array}\,} \right| = 0$

Standard 12

Mathematics

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