If determinant left| {begin{array}{*{20}{c}}{a, + ,p}&{1, + ,x}&{u, + ,f} {b, + ,q}&{m,

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3 and 4 .Determinants and Matrices

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If the determinant $\left| {\begin{array}{*{20}{c}}{a\, + \,p}&{1\, + \,x}&{u\, + \,f}\\ {b\, + \,q}&{m\, + \,y}&{v\, + \,g}\\{c\, + \,r}&{n\, + \,z}&{w\, + \,h}\end{array}} \right|$ splits into exactly $K$ determinants of order $3$, each element of which contains only one term, then the value of $K$, is

A

$6$

B

$8$

C

$9$

D

$12$

Solution

Divide $c_1$ by $x, c_2$ by y and $c_3$ by $z$ and use $c_1 \rightarrow c_1 + c_2 + c_3$

Standard 12

Mathematics

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(IIT-2018)