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Provide solution for RD Sharma maths class 12 chapter Determinants exercise multiple choise question 2

Answers (1)


Correct option (d)


Using the properties of determinant.


        \begin{vmatrix} a+b &c+d \\ e+f &g+h \end{vmatrix}


We know that,

 If each element of a row or column of determinant is expressed as a sum of two or more terms, then the determinant can be expressed as the sum of two or more determinant.

So,\; \; \; \; \begin{vmatrix} a+b &c+d \\ e+f &g+h \end{vmatrix}=\begin{vmatrix} a+b &c \\ e+f &g \end{vmatrix}+\begin{vmatrix} a+b &d \\ e+f &h \end{vmatrix}

                                              =\left | a\, c\, e\, g \right |+\left | b\, c\, f\, g \right |+\left | a\, d\, e\, h \right |+\left | b\, d\, f\, h \right |


        So,\; \; \; \; \begin{vmatrix} a+b &c+d \\ e+f &g+h \end{vmatrix}\neq \begin{vmatrix} a &c \\ e &g \end{vmatrix}+\begin{vmatrix} b &d \\ f &h \end{vmatrix}

Hence option (d) is correct.

Posted by

Gurleen Kaur

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