Which of following determinant (s) vanish (es) ?

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3 and 4 .Determinants and Matrices

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Which of the following determinant $(s)$ vanish $(es)$ ?

A$\left| {\,\begin{array}{*{20}{c}}1&{b\,c}&{b\,c\,\,(b\,\, + \,\,c)}\\1&{c\,a}&{c\,a\,\,(c\,\, + \,\,a)}\\1&{a\,b}&{a\,b\,\,(a\,\, + \,\,b)}\end{array}\,} \right|$

B$\left| {\,\begin{array}{*{20}{c}}1&{a\,b}&{{\textstyle{1 \over a}}\,\, + \,\,{\textstyle{1 \over b}}}\\1&{b\,c}&{{\textstyle{1 \over b}}\,\, + \,\,{\textstyle{1 \over c}}}\\ 1&{c\,a}&{{\textstyle{1 \over c}}\,\, + \,\,{\textstyle{1 \over a}}}\end{array}\,} \right|$

C$\left| {\,\begin{array}{*{20}{c}}0&{a\,\, - \,\,b}&{a\,\, - \,\,c}\\{b\,\, - \,\,a}&0&{b\,\, - \,\,c}\\{c\,\, - \,\,a}&{c\,\, - \,\,b}&0\end{array}\,} \right|$

DAll of the above

Solution

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Standard 12

Mathematics

If $\left[ {\begin{array}{{20}{c}}2&{ – 3}\\4&0\end{array}} \right] – \left[ {\begin{array}{{20}{c}}a&c\\b&d\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}1&4\\2&{ – 5}\end{array}} \right]$, then $(a,b,c,d) = $

easy

If $A=\left[\begin{array}{cc}\alpha & \beta \\ \gamma & -\alpha\end{array}\right]$ is such that $A^{2}=I$, then

medium

If $A = \left( {\begin{array}{*{20}{c}}2&{ – 1}\\{ – 1}&2\end{array}} \right)$ and $I$ is the unit matrix of order $2$, then ${A^2}$ equals

easy

If $A$ is an idempotent matrix, then $(I + A)^4$ is (where $I$ is identity matrix of order same as $A$ )

hard

If $A = \left[ {\begin{array}{*{20}{c}}4&2\\{ – 1}&1\end{array}} \right]$and $I$ is the identity matrix of order $2$, then $(A – 2I)(A – 3I) = $

easy

Which of the following determinant $(s)$ vanish $(es)$ ?

Solution

Similar Questions

If $\left[ {\begin{array}{*{20}{c}}2&{ – 3}\\4&0\end{array}} \right] – \left[ {\begin{array}{*{20}{c}}a&c\\b&d\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}1&4\\2&{ – 5}\end{array}} \right]$, then $(a,b,c,d) = $

If $A=\left[\begin{array}{cc}\alpha & \beta \\ \gamma & -\alpha\end{array}\right]$ is such that $A^{2}=I$, then

If $A = \left( {\begin{array}{*{20}{c}}2&{ – 1}\\{ – 1}&2\end{array}} \right)$ and $I$ is the unit matrix of order $2$, then ${A^2}$ equals

If $A$ is an idempotent matrix, then $(I + A)^4$ is (where $I$ is identity matrix of order same as $A$ )

If $A = \left[ {\begin{array}{*{20}{c}}4&2\\{ – 1}&1\end{array}} \right]$and $I$ is the identity matrix of order $2$, then $(A – 2I)(A – 3I) = $

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If $\left[ {\begin{array}{{20}{c}}2&{ – 3}\\4&0\end{array}} \right] – \left[ {\begin{array}{{20}{c}}a&c\\b&d\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}1&4\\2&{ – 5}\end{array}} \right]$, then $(a,b,c,d) = $