આપેલ પૈકી વિસંમિત શ્રેણિક મેળવો.

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3 and 4 .Determinants and Matrices

easy

આપેલ પૈકી વિસંમિત શ્રેણિક મેળવો.

A

$\left[ {\begin{array}{*{20}{c}}0&4&5\\{ - 4}&0&{ - 6}\\{ - 5}&6&0\end{array}} \right]$

B

$\left[ {\begin{array}{*{20}{c}}1&4&5\\{ - 4}&1&{ - 6}\\{ - 5}&6&1\end{array}} \right]$

C

$\left[ {\begin{array}{*{20}{c}}{\,\,1}&4&5\\{ - 4}&2&{ - 6}\\{ - 5}&6&3\end{array}} \right]$

D

$\left[ {\begin{array}{*{20}{c}}{i + 1}&4&5\\{ - 4}&i&{ - 6}\\{ - 5}&6&i\end{array}} \right]$

Solution

(a) In a skew-symmetrix matrix ${a_{ij}} = – {a_{ji}}\rlap{–} \vee i,\,j = 1,\,2,\,3$ for $j = i,\,\,{a_{ii}}$ =$ – {a_{ji}}$

==> each ${a_{ii}} = 0$.

Hence the matrix $\left[ {\begin{array}{*{20}{c}}0&4&5\\{ – 4}&0&{ – 6}\\{ – 5}&6&0\end{array}} \right]$ is skew-symmetric.

Standard 12

Mathematics

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જો ${\left\{ {\left( \begin{gathered}
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(JEE MAIN-2019)