Find the inverse of each of the matrices(if it exists). \(\begin{bmatrix}2&1&3\\4&-1&0\\-7&2&1\end{bmatrix}\)
Find the inverse of each of the matrices(if it exists). \(\begin{bmatrix}2&1&3\\4&-1&0\\-7&2&1\end{bmatrix}\)
Solution and Explanation
Let A=\(\begin{bmatrix}2&1&3\\4&-1&0\\-7&2&1\end{bmatrix}\)
We have IAI=2(-1-0)-1(4-0)+3(8-7)
=-2-4+3
=-3
Now A11=-1-0=-1, A12=-(4-0), A13=8-7=1
A21=-(1-6)=5, A22=2+21=23, A23=-(-(4+7)=-11
A31=0+3=3, A32=-(0-12)=12,A33=-2-4=-6
therefore adj A=\(\begin{bmatrix}-1&5&3\\-4&23&12\\1&-11&-6\end{bmatrix}\)
so A-1=\(\frac{1}{\mid A\mid}\)adj A=\(-\frac{1}{3}\) \(\begin{bmatrix}-1&5&3\\-4&23&12\\1&-11&-6\end{bmatrix}\)
Top Questions on Determinants
- Let
\[ f(x)=\int \frac{7x^{10}+9x^8}{(1+x^2+2x^9)^2}\,dx,\quad x > 0, \] and
\[ A= \begin{bmatrix} 0 & 0 & 1 \\ \frac{1}{4} & f'(1) & 1 \\ \alpha & 4 & 1 \end{bmatrix}. \] If \( B=\operatorname{adj}(\operatorname{adj} A) \), then the value of \( \alpha \) for which \( \det(B)=1 \) is
- JEE Main - 2026
- Mathematics
- Determinants
- Let $P$ and $Q$ be any two $3\times3$ matrices where $P=[p_{ij}]_{3\times3}$, $Q=[q_{ij}]_{3\times3}$ such that $q_{ij}=2^{\,i+j-1}p_{ij}$. Find $|\operatorname{adj}(\operatorname{adj}P)|$.
- JEE Main - 2026
- Mathematics
- Determinants
- Let $P$ and $Q$ be any two $3\times3$ matrices where $P=[p_{ij}]_{3\times3}$, $Q=[q_{ij}]_{3\times3}$ such that $q_{ij}=2^{\,i+j-1}p_{ij}$. Find $|\operatorname{adj}(\operatorname{adj}P)|$.
- JEE Main - 2026
- Mathematics
- Determinants
- Consider the function given below and pick one or more CORRECT statement(s) from the following choices.
\[ f(x) = x^3 - \frac{15}{2} x^2 + 18x + 20 \] A settling chamber is used for the removal of discrete particulate matter from air with the following conditions. Horizontal velocity of air = 0.2 m/s; Temperature of air stream = 77°C; Specific gravity of particle to be removed = 2.65; Chamber length = 12 m; Chamber height = 2 m; Viscosity of air at 77°C = 2.1 × 10\(^{-5}\) kg/m·s; Acceleration due to gravity (g) = 9.81 m/s²; Density of air at 77°C = 1.0 kg/m³; Assume the density of water as 1000 kg/m³ and Laminar condition exists in the chamber.
The minimum size of particle that will be removed with 100% efficiency in the settling chamber (in $\mu$m is .......... (round off to one decimal place).
Questions Asked in CBSE CLASS XII exam
If vector \( \mathbf{a} = 3 \hat{i} + 2 \hat{j} - \hat{k} \) \text{ and } \( \mathbf{b} = \hat{i} - \hat{j} + \hat{k} \), then which of the following is correct?
- Find the value of $x$, if \[ \begin{bmatrix} 1 & 3 & 2 \\ 2 & 5 & 1 \\ 15 & 3 & 2 \end{bmatrix} \begin{bmatrix} 1 \\ x \\ 2 \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix} \]
- Two point charges of \( -5\,\mu C \) and \( 2\,\mu C \) are located in free space at \( (-4\,\text{cm}, 0) \) and \( (6\,\text{cm}, 0) \) respectively.
(a) Calculate the amount of work done to separate the two charges at infinite distance.
(b) If this system of charges was initially kept in an electric field \[ \vec{E} = \frac{A}{r^2}, \text{ where } A = 8 \times 10^4\, \text{N}\,\text{C}^{-1}\,\text{m}^2, \] calculate the electrostatic potential energy of the system.- CBSE CLASS XII - 2025
- Electrostatics
- 4,000 shares of ₹ 10 each were forfeited for non-payment of second and final call money of ₹ 2 per share. The minimum amount that the company must collect at the time of reissue of these shares will be :
- CBSE CLASS XII - 2025
- Accounting for Share Capital
- If $y = a \cos(\log x) + b \sin(\log x)$, then $x^2y'' + xy'1$ is:
- CBSE CLASS XII - 2025
- Continuity and differentiability