The inverse of the matrix [ * 20 c 3& - 2 1&4 ]is - Vidyadip

MCQ

The inverse of the matrix $\left[ {\begin{array}{*{20}{c}}3&{ - 2}\\1&4\end{array}} \right]$is

✓
$\left[ {\begin{array}{*{20}{c}}{\frac{4}{{14}}}&{\frac{2}{{14}}}\\{\frac{{ - 1}}{{14}}}&{\frac{3}{{14}}}\end{array}} \right]$
B
$\left[ {\begin{array}{*{20}{c}}{\frac{3}{{14}}}&{\frac{{ - 2}}{{14}}}\\{\frac{1}{{14}}}&{\frac{4}{{14}}}\end{array}} \right]$
C
$\left[ {\begin{array}{*{20}{c}}{\frac{4}{{14}}}&{\frac{{ - 2}}{{14}}}\\{\frac{1}{{14}}}&{\frac{3}{{14}}}\end{array}} \right]$
D
$\left[ {\begin{array}{*{20}{c}}{\frac{3}{{14}}}&{\frac{2}{{14}}}\\{\frac{1}{{14}}}&{\frac{4}{{14}}}\end{array}} \right]$

✓

Answer

Correct option: A.

$\left[ {\begin{array}{*{20}{c}}{\frac{4}{{14}}}&{\frac{2}{{14}}}\\{\frac{{ - 1}}{{14}}}&{\frac{3}{{14}}}\end{array}} \right]$

a
(a) Let $A = \left[ {\begin{array}{*{20}{c}}3&{ - 2}\\1&4\end{array}} \right]\, \Rightarrow |A| = 14$
$\therefore $ $adj\,A = \left[ {\begin{array}{*{20}{c}}4&2\\{ - 1}&3\end{array}} \right]$ $ \Rightarrow $ ${A^{ - 1}} = \left[ {\begin{array}{*{20}{c}}{\frac{4}{{14}}}&{\frac{2}{{14}}}\\{\frac{{ - 1}}{{14}}}&{\frac{3}{{14}}}\end{array}} \right]$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 3 and 4 . determinant and metrices→3 and 4 . determinant and metrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\int_0^1 {x\log \left( {1 + \frac{x}{2}} \right)} \,dx = a + b\log \frac{2}{3},$ then

${d \over {dx}}\,\,\left[ {{{\tan }^{ - 1}}\left( {{{\sqrt x (3 - x)} \over {1 - 3x}}} \right)} \right] =$

The value of $x,$ if $\left| {\,\begin{array}{*{20}{c}}{ - x}&1&0\\1&{ - x}&1\\0&1&{ - x}\end{array}\,} \right| = 0 $ is equal to

The integral $\int {\sqrt {1 + 2\cot \,x\,\left( {\cos ec\,x + \cot \,x} \right)} \,dx} $ $\left( {0 < x < \frac{\pi }{2}} \right)$ is equal to ( where $C$ is a constant of integration)

If the area bounded by the curve $2 y^2=3 x$, lines $x+y=3, y=0$ and outside the circle $(x-3)^2+y^2=2$ is $A$, then $4(\pi+4 A )$ is equal to $.........$.

If x^y = e^x-y then $\frac{\text{dy}}{\text{dx}}$ is:

$\frac{1+\text{x}}{1+\log\text{x}}$
$\frac{1-\log\text{x}}{1+\log\text{x}}$
$\text{Not defined.}$
$\frac{\log\text{x}}{(1+\log\text{x})^2}$

If three vectors $a = 12i + 4j + 3k , b = 8i - 12j - 9k$ and $c = 33i - 4j - 24k$ represents $a$ cube, then its volume will be

If $f(x)=$ $7{e^{{{\sin }^2}x}} - {e^{{{\cos }^2}x}} + 2$, then,$\sqrt {7{f_{\min }} + {f_{\max }}}$ is equal to

Let $a$ , $b$ , $c$ are non real numbers satisfying equation $x^5 = 1$ and $S$ be the set of all non-invertible matrices of the form $\left[ {\begin{array}{*{20}{c}}
1&a&b \\
w&1&c \\
{{w^2}}&w&1
\end{array}} \right],\,\,\,\,w = {e^{\frac{{i\,2\pi }}{5}}}$ . Then the number of distinct matrices in the set $S$ is

If $A = \left[ {\begin{array}{*{20}{c}}1&2&1\\0&1&{ - 1}\\3&{ - 1}&1\end{array}} \right]$, then