Download App

Question Bank [2022] — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsQuestion Bank [2022]2 Marks
Question
If $A=\left[\begin{array}{ll}2 & 4 \\ 1 & 3\end{array}\right]$ and $B=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]$ then find $\left(A^{-1} B^{-1}\right)$
✓

Answer

$\begin{array}{l}\left(A^{-1} B^{-1}\right)=(B A)^{-1} \ldots . .\left[\because(A B)^{-1}=B^{-1} A^{-1}\right] \end{array}$
$ \therefore A=\left[\begin{array}{ll}2 & 4 \\ 1 & 3\end{array}\right] $
$ A=(2 \times 3)-(4 \times 1) $
$ A=6-4 \\ A=2 $
$ \therefore B=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right] $
$ B=(1 \times 1)-(1 \times 0)$
$ B=1-0$ 
$B=1$
$\left(A^{-1} B^{-1}\right)=\frac{1}{|A|}(\operatorname{adj} A) \cdot \frac{1}{|B|}(\operatorname{adj} B)$
$ =\frac{1}{2}\left[\begin{array}{cc}3 & -4 \\ -1 & 2\end{array}\right] \times \frac{1}{1}\left[\begin{array}{cc}1 & -1 \\ 0 & 1\end{array}\right] $
$ =\frac{1}{2}\left[\begin{array}{cc}3 & -4 \\ -1 & 2\end{array}\right]\left[\begin{array}{cc}1 & -1 \\ 0 & 1\end{array}\right] \\ =\frac{1}{2}\left[\begin{array}{cc}3 & -7 \\ -1 & 3\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 "Solve the Following Question.(2 Marks)" from Question Bank [2022]→Question Bank [2022] — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Let A be a $3 × 3$ square matrix, such that A (adj A) = 2I, where I is the identity matrix. Write the value of |adj A|.
→
In a parliament election, a political party hired a public relations firm to promote its candidates in three ways - telephone, house calls and letters. The cost per contact (in paisa) is given in matrix A as
$\text{A}=\begin{bmatrix}140&\text{Telephone}\\200&\text{House calls}\\150&\text{Letters}\end{bmatrix}$
The number of contacts of each type made in two cities X and Yis given in the matrix B as
$\begin{matrix}\text{Telephone}&\text{House calls}&\text{Letters}\end{matrix}\\\text{B}=\begin{bmatrix}1000&500&5000\\3000&1000&10000\end{bmatrix}\begin{matrix}\text{City X}\\\text{City Y}\end{matrix}$
Find the total amount spent by the party in the two cities.
What should one consider before casting his/ her vote - party's promotional activity of their social activities?
→
If $f: R \rightarrow R$ defined by $f(x)=3 x-4$ is invertible, then write $f^{-1}(x)$.
→
If $\begin{bmatrix}2&1&3 \end{bmatrix}$ $\begin{pmatrix}-1&0&-1\\-1&1&0\\0&1&1 \end{pmatrix}\begin{pmatrix}1\\0\\-1 \end{pmatrix}=\text{A},$ then write the order of matrix A.
→
Write a value of $\int\sin^3\text{x}\cos\text{x dx}$
→
Find the solution set of inequalities 0 ≤ x ≤ 5, 0 ≤ 2y ≤ 7
→
If $y=\log \left[\cos \left(x^5\right)\right]$ then find $\frac{ d y}{ d x}$
→
$\int \frac{\log (\log x)}{x} d x$
→
Integrate the following functions w.r.t x:

$\frac{\cos 3 x-\cos 4 x}{\sin 3 x+\sin 4 x}$

→
Water is being poured at the rate of $36\ m^3/sec$ in to a cylindrical vessel of base radius $3$ meters. Find the rate at which water level is rising
→