If cofactor C _ i j represent for element p_ i j , of matrix P = … - Vidyadip

MCQ

If cofactor $C _{i j}$ represent for element $p_{i j}$, of matrix $P =\left[\begin{array}{ccc}1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & 2 & 4\end{array}\right]$ then value of $C_{31} . C_{23}$ is $:$

✓
$5$
B
$24$
C
$-24$
D
$-5$

✓

Answer

Correct option: A.

$5$

$\begin{aligned} & C_{31}=(-1)^{3+1}\left|\begin{array}{cc}-1 & 2 \\ 2 & -3\end{array}\right|=3-4=-1 \end{aligned} $
$ C_{23}=(-1)^{2+3}\left|\begin{array}{cc}1 & -1 \\ 3 & 2\end{array}\right|=-(2+3)=-5 $
$ \text { Hence } C_{31} \cdot C_{23} =(-1)(-5) =5$

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 Determinants→Determinants — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The vectors $2\hat{\text{i}}+3\hat{\text{j}}-4\hat{\text{k}}$ and $\text{a}\hat{\text{i}}+\text{b}\hat{\text{j}}+\text{c}\hat{\text{k}}$ are perpendicular if :

If $\text{P(B)}=\frac{3}{5},\text{P}(\text{A}|\text{B})=\frac{1}{2}$ and $\text{P}(\text{A}\cup\text{B})=\frac{4}{5},$ then $\text{P}(\text{B}|\overline{\text{A}})=$

Let $f(x) = \frac{{1 - \tan x}}{{4x - \pi }},\;x \ne \frac{\pi }{4},\;\;x \in \left[ {0,\frac{\pi }{2}} \right]$, If $f(x)$ is continuous in $\left[ {0,\frac{\pi }{2}} \right]$, then $f\left( {\frac{\pi }{4}} \right)$ is

Choose the correct answer from the given four options.If matrix $A=\left[a_{i j}\right] 2 \times 2$, where $a_{i j}=1,$ if $i \neq j$ and 0 if $i=j$ then $A^2$ equal to :

What is direction of vector $\vec{\text{a}}$ if it is multiplied with $-\lambda$:

A particle moves along the curve $y = x^{3/2}$ in the first quadrant in such a way that its distance from the origin increases at the rate of $11$ units per second. The value of $\frac{{dx}}{{dt}}$ when $x = 3$ is

Let $\mathrm{X}$ be the set of all five digit numbers formed using $1,2,2,2,4,4,0$. For example, $22240$ is in $\mathrm{X}$ while $02244$ and $44422$ are not in $X$. Suppose that each element of $X$ has an equal chance of being chosen. Let $\mathrm{p}$ be the conditional probability that an element chosen at random is a multiple of $20$ given that it is a multiple of $5$ . Then the value of $38 p $ is equal to

$\sin^{-1}(1-\text{x})-2\sin^{-1}\text{x}=\frac{\pi}{2}$

If $f: R \rightarrow R$ be given by $f(\text{x})=(3-\text{x}^3)^{\frac{1}{3}},$ then $fof(x)$ is:

$\int\limits_0^\pi {{e^{{{\cos }^4}x}}} . \cos^5(2n + 1)x \,dx, (n \in I)$ is equal to