Download App

Question Bank [2022] — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Question Bank [2022]3 Marks
Question
If $A=\left[\begin{array}{ll}3 & 1 \\ 1 & 5\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & 2 \\ 5 & -2\end{array}\right]$, then verify $|A B|=|A||B|$
✓

Answer

$\begin{array}{l}A B=\left[\begin{array}{ll}3 & 1 \\ 1 & 5\end{array}\right]\left[\begin{array}{cc}1 & 2 \\ 5 & -2\end{array}\right] \end{array} $
$ =\left[\begin{array}{cc}3+5 & 6-2 \\ 1+25 & 2-10\end{array}\right]  $
$ =\left[\begin{array}{cc}8 & 4 \\ 26 & -8\end{array}\right]  $
$ \therefore A B=\left|\begin{array}{cc}8 & 4 \\ 26 & 8\end{array}\right|  $
$ =-64-104  $
$ =-168  $
$ |A|=\left|\begin{array}{ll}3 & 1 \\ 1 & 5\end{array}\right|   $
$=15-1  $
$ =14$
$\begin{array}{l}| B |=\left|\begin{array}{cc}1 & 2 \\ 5 & -2\end{array}\right| \end{array} $
$ =-2-10 $
$ =-12 $
$ \therefore|A||B|=14(-12)=-168 $
$ \therefore|A B|=|A||B|$

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.(3 Marks)" from Question Bank [2022]→Question Bank [2022] — all question types→Maths (commerce) STD 12 Commerce / Arts question papers→Maharashtra Board STD 12 Commerce / Arts question papers→Maharashtra Board question paper generator→

Similar questions

if $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 3 & 1\end{array}\right]$, then reduce it to unit matrix by row tranformation.
→
If the demand function is $D =\left(\frac{p+6}{p-3}\right)$, find the elasticity of demand at $p =4$.
→
If $A=\left[\begin{array}{ccc}-1 & 1 & 1 \\ 2 & 3 & 0 \\ 1 & -3 & 1\end{array}\right], B=\left[\begin{array}{lll}2 & 1 & 4 \\ 3 & 0 & 2 \\ 1 & 2 & 1\end{array}\right]$. State whether $A B=B A$ ? Justify your answer.
→
Evaluate the following integrals: $\int_0^1 \log \left(\frac{1}{x}-1\right) \cdot d x$
→
Find the cost living index number by the weighted aggregate method.
GROUPFOODCLOTHINGFUEL & LIGHTINGHOUSE RENTMISCELLANEOUS
I78801106090
W53426
→
Find $\frac{d y}{d x}$ if, :
$
y=e^{x^x}
$
→
Find the inverse of matrix $B=\left[\begin{array}{lll}3 & 1 & 5 \\ 2 & 7 & 8 \\ 1 & 2 & 5\end{array}\right]$ by using adjoint method
→
A foreman wants to process 4 different jobs on three machines: a shaping machine, a drilling machine, and a tapping, the sequence of operations being shaping-drilling-tapping. Decide the optimal sequence for the four jobs to minimize the total elapsed time. Also, find the total elapsed time and the idle time for every machine.
JobSHAPING (MINUTES)DRILLING (MINUTES)TRAPPING (MINUTES)
113318
21884
38613
42368
→
You are given the following information about advertising expenditure and sales.
Advertisement expenditure (Rs.in lakh)Sales (Rs.in lakh)
Arithmetic mean1090
Standard deviation312
Correlation coefficient between X and Y is 0.8
(i) Obtain two regression equations.
(ii) What is the likely sales when the advertising budget is ₹ 15 lakh?
(iii) What should be the advertising budget if the company wants to attain sales target of ₹ 120 lakh?
→
Evaluate $\int \frac{2 e ^x+5}{2 e ^x+1} d x$
→