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  • If the determinant <img alt="\begin{vmatrix} a+p &\l+x & u+f \\ b+q& m+y & v+g\\ c+r& n+z & w+h \end{vmatrix}" src="https://learn.careers360.com/latex-image/?%5Cbegin%7

If the determinant \begin{vmatrix} a+p &\l+x & u+f \\ b+q& m+y & v+g\\ c+r& n+z & w+h \end{vmatrix} splits into exactly K determinants of order 3, each element of which contains only one term, then the value of K =

Option: 1 6

Option: 2 7

Option: 3 8

Option: 4 9

Answers (1)

best_answer

 

Property of determinant -

If each element in a row ( or column ) of a determinant is written as the sum of two or more terms then the determinant can be written as the sum of two or more determinants

- wherein

 

 

\begin{vmatrix} a+p &\l+x & u+f \\ b+q& m+y & v+g\\ c+r& n+z & w+h \end{vmatrix}=\begin{vmatrix} a+p & \ l+x & u\\ b+q& m+y &v \\ c+r&n+z &w \end{vmatrix}+\begin{vmatrix} a+p &\ l+x & f\\ b+q& m+y &g \\ c+r&n+z &h \end{vmatrix}

=\begin{vmatrix} a+p & \ l & u \\ b+q& m & v\\ c+r& n & w \end{vmatrix}+\begin{vmatrix} a+p & x & u \\ b+q& y &v \\ c+r& z & w \end{vmatrix}+\begin{vmatrix} a+p &\ l & f \\ b+q & m &g \\ c+r& n &h \end{vmatrix}+\begin{vmatrix} a+p &x &f \\ b+q &y &g \\ c+r& z &h \end{vmatrix}

Now each det. may splits in 2 det.

So, total determinants are 8.

 

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Gunjita

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