In-a-third-order-determinant-each-element-of-the-first-column-consists-of-sum-of-2-terms-each-element-of-the-second-column-consists-of-sum-of-3-terms-and-each-element-of-the-third-column-consists-of

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Question Number 15158 by arnabpapu550@gmail.com last updated on 08/Jun/17

$$\mathrm{In}\mathrm{a}\mathrm{third}\mathrm{order}\mathrm{determinant},\mathrm{each}$$$$\mathrm{element}\mathrm{of}\mathrm{the}\mathrm{first}\mathrm{column}\mathrm{consists}\mathrm{of}$$$$\mathrm{sum}\mathrm{of}2\mathrm{terms},\mathrm{each}\mathrm{element}\mathrm{of}\mathrm{the}$$$$\mathrm{second}\mathrm{column}\mathrm{consists}\mathrm{of}\mathrm{sum}\mathrm{of}3\mathrm{terms}$$$$\mathrm{and}\mathrm{each}\mathrm{element}\mathrm{of}\mathrm{the}\mathrm{third}\mathrm{column}$$$$\mathrm{consists}\mathrm{of}\mathrm{sum}\mathrm{of}4\mathrm{terms}.\mathrm{Then}\mathrm{it}\mathrm{can}$$$$\mathrm{be}\mathrm{decomposed}\mathrm{into}n\mathrm{determinants},$$$$\mathrm{where}n\mathrm{has}\mathrm{the}\mathrm{value}$$$$\mathrm{Ans}=24$$

Commented by 1kanika# last updated on 07/Jun/17

$$\mathrm{n}+1\mathrm{may}\mathrm{be}$$

Commented by arnabpapu550@gmail.com last updated on 08/Jun/17

$$\mathrm{But}\mathrm{its}\mathrm{answer}\mathrm{is}24$$

Commented by prakash jain last updated on 08/Jun/17

$$2\times 3\times 4$$$$e.g$$$$\left[\begin{array}{cc}a+b& c+d\\ e+f& g+h\end{array}\right]$$$$=\left[\begin{array}{cc}a& c+d\\ e& g+h\end{array}\right]+\left[\begin{array}{cc}b& c+d\\ f& g+h\end{array}\right]$$$$=\left[\begin{array}{cc}a& c\\ e& g\end{array}\right]+\left[\begin{array}{cc}a& d\\ e& h\end{array}\right]+\left[\begin{array}{cc}b& c\\ f& g\end{array}\right]+\left[\begin{array}{cc}b& d\\ f& h\end{array}\right]$$

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