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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
