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

Correct option (d)

Hint:

Using the properties of determinant.

Given:

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

Solution:

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.

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

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

Hence,

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

Hence option (d) is correct.