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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 $A = \left[ {\begin{array}{*{20}{c}}0&2\\3&{ - 4}\end{array}} \right]$ and $kA = \left[ {\begin{array}{*{20}{c}}0&{3a}\\{2b}&{24}\end{array}} \right]$, then the values of $k, a, b$ are respectively
  • A
    $ - \,6, - \,12, - \,18$
  • B
    $-6, 4, 9$
  • ✓
    $ - \,6, - \,4, - \,9$
  • D
    $-6, 12, 18$
✓

Answer

Correct option: C.
$ - \,6, - \,4, - \,9$
c
(c) Given, $kA = \left[ {\,\begin{array}{*{20}{c}}0&{3a}\\{2b}&{24}\end{array}\,} \right]$==> $k\,\,\left[ {\begin{array}{*{20}{c}}0&2\\3&{ - 4}\end{array}} \right]\, = \,\left[ {\begin{array}{*{20}{c}}0&{3a}\\{2b}&{24}\end{array}} \right]$

==> $2k = 3a,\,3k = 2b,\, - 4k = 24$

==> $a = \frac{{2k}}{3},\,\,\,b = \frac{{3k}}{2},\,k = - 6$

$ \Rightarrow $ $k = - 6,\,\,a = - 4,\,b = - 9$.

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