Download App

Matrics — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsMatrics2 Marks
MCQ
The element of second row and third column in the inverse of $\left[\begin{array}{ccc}1 & 2 & 1 \\ 2 & 1 & 0 \\ -1 & 0 & 1\end{array}\right]$ is
  • A
    $-2$
  • ✓
    $-1$
  • C
    $1$
  • D
    $2$
✓

Answer

Correct option: B.
$-1$
(B) Let $A=\left[\begin{array}{ccc}1 & 2 & 1 \\ 2 & 1 & 0 \\ -1 & 0 & 1\end{array}\right] \Rightarrow|A|=-2 \neq 0$
Now, co-factor of element $a _{32}$ of $A = A _{32}$
$\therefore \quad A _{32}=(-1)^{3+2}\left|\begin{array}{ll}1 & 1 \\ 2 & 0\end{array}\right|=2$
$\therefore \quad$ Element $a _{23}$ of $A ^{-1}=\frac{ A _{32}}{|A|}=\frac{2}{-2}=-1$
Alternate method:
$|A|=-2 \neq 0$
$\operatorname{adj} A=\left[\begin{array}{ccc}1 & -2 & -1 \\ -2 & 2 & 2 \\ 1 & -2 & -3\end{array}\right]$
$\therefore \quad A^{-1}=\left[\begin{array}{ccc}-\frac{1}{2} & 1 & \frac{1}{2} \\ 1 & -1 & -1 \\ -\frac{1}{2} & 1 & \frac{3}{2}\end{array}\right]$
$\therefore \quad$ Element $a _{23}$ of $A ^{-1}=-1$.

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 "MCQ" from Matrics→Matrics — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

If $\text{A}=\begin{bmatrix}\alpha&\beta\\\gamma&-\alpha\end{bmatrix}$ is such that $A^2 = I$, then:
→
If $A$ and $B$ are two events such that $\text{P(A)}=\frac{4}{5},$ and $\text{P}(\text{A}\cap\text{B})=\frac{7}{10},$ then $P(B|A) =$
→
The direction ratios of the line which is perpendicular to the two lines
$\frac{x-7}{2}=\frac{y+17}{-3}=\frac{z-6}{1}$ and $\frac{x+5}{1}=\frac{y+3}{2}=\frac{z-6}{-2}$ are
→
The value of $\sin \left(2 \tan ^{-1}\left(\frac{1}{3}\right)\right)+\cos \left(\tan ^{-1} 2 \sqrt{2}\right)=$
→
The function $\text{f(x)}=|\cos\text{x}|$ is:
→
If $\log_e 4 = 1.3868$, then $\log_e 4.01 =$
→
Write verbally ∼p∨q where
p: She is beautiful; q: She is clever
→
The number of distinct real values of $\lambda$, for which the vectors $-\lambda^2 \hat{i}+\hat{j}+\hat{k}, \hat{i}-\lambda^2 \hat{j}+\hat{k}$ and $\hat{ i }+\hat{ j }-\lambda^2 \hat{ k }$ are coplanar, is
→
Area lying first quadrant and bounded by the circle $x^2 + y^2 = 4$ and the line $x = 0$ and $x = 2$, is:
→
If $\sin 6 \theta+\sin 4 \theta+\sin 2 \theta=0$, then the general value of $\theta$ is
Where, n is an interger.
→