3 and 4 .Determinants and Matrices
easy

यदि $a \ne 6,b,c$ सारणिक $\left| {\,\begin{array}{*{20}{c}}a&{2b}&{2c}\\3&b&c\\4&a&b\end{array}\,} \right| = 0,$ तो $abc = $

A

$a + b + c$

B

$0$

C

${b^3}$

D

$ab + bc$

Solution

(c) $\left| {\,\begin{array}{*{20}{c}}
  a&{2b}&{2c} \\ 
  3&b&c \\ 
  4&a&b 
\end{array}\,} \right| = 0 =  > \left| {\,\begin{array}{*{20}{c}}
  {a – 6}&0&0 \\ 
  3&b&c \\ 
  4&a&b 
\end{array}\,} \right| = 0$ $[R_1 → R_1 -2R_2]$

==> $(a – 6)({b^2} – ac) = 0 \Rightarrow {b^2} – ac = 0$ $a \ne 6$

$\therefore $ $ac = {b^2} \Rightarrow abc = {b^3}.$

Standard 12
Mathematics

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