If A = [ * 20 c 0&2 3& - 4 ] and kA = [ * 20 c 0& 3a 2b & 24 ], t… - Vidyadip

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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