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3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
MCQ
If $a \ne 6,b,c$ satisfy $\left| {\,\begin{array}{*{20}{c}}a&{2b}&{2c}\\3&b&c\\4&a&b\end{array}\,} \right| = 0,$then $abc = $
  • A
    $a + b + c$
  • B
    $0$
  • ✓
    ${b^3}$
  • D
    $ab + bc$
✓

Answer

Correct option: C.
${b^3}$
c
(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 $ $ac = {b^2} \Rightarrow abc = {b^3}.$

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