Download App

Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices3 Marks
Question
Find the values of $a$ and below
$
\left[\begin{array}{cc}
a+3 & b^2+2 \\
0 & -6
\end{array}\right]=\left[\begin{array}{cc}
2 a+1 & 3 b \\
0 & b^2-5 b
\end{array}\right]
$
✓

Answer

$
\left[\begin{array}{cc}
a+3 & b^2+2 \\
0 & -6
\end{array}\right]=\left[\begin{array}{cc}
2 a+1 & 3 b \\
0 & b^2-5 b
\end{array}\right]
$
comparing the corresponding elements
$
\begin{aligned}
& a+3=2 a+1 \\
& \Rightarrow 2 a-a=3-1 \\
& \Rightarrow a=2 \\
& b^2+2=3 b \\
& \Rightarrow b^2-3 b+2=0 \\
& \Rightarrow b^2-b-2 b+2=0 \\
& \Rightarrow b(b-1)-2(b-1)=0 \\
& \Rightarrow(b-1)(b-2)=0 .
\end{aligned}
$
Either $b-1=0$,
then $b=1$
or
$
b-2=0 \text {, }
$
then $b=2$
Hence $a=2, b=2$ or 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 "[3 marks sum]" from Matrices→Matrices — all question types→Mathematics STD 10 question papers→ICSE Board STD 10 question papers→ICSE Board question paper generator→

Similar questions

A man tosses two different coins (one of Rs 2 and another of Rs 5) simultaneously. What is the probability that he gets:  at least one head?  
→
In the following figure; If AB = AC then prove that BQ = CQ.
→
Two different dice are thrown at the same time. Find the probability of getting :
(iii) a sum of at least 11 
→
In the figure, given below, it is given that $AB$ is perpandiculer to $BD$ and is of length $X$ metres. $DC = 30m .\angle ADB = 30^\circ$ and $\angle ACB = 45^\circ . $Without using tables, find $X$​​​​​​​
→
Draw histogram ffor the following distributtions:
Class Marks 16 24 32 40 48 56 64
Frequency 8 12 15 18 25 19 10
→
A ball is chosen from a bag that contains 30 balls numbered from 1 to 30 . What is the probability that the ball chosen will have a number that is divisible by 3 ?
→
(i) Plot the points A (3, 5) and B (-2, -4). Use 1 cm = 1 unit on both the axes.

(ii) A’ is the image of A when reflected in the x-axis. Write down the co-ordinates of A’ and plot it on the graph paper.

(iii) B’ is the image of B when reflected in the y-axis, followed by reflection in the origin. Write down the co-ordinates of B’ and plot it on the graph paper.

(iv) Write down the geometrical name of the figure AA’BB’.

(v) Name the invariant points under reflection in the x-axis.

→
In the following figures, O is the centre of the circle. Find the values of a, b and c.
→
The volume of a sphere is $38808 \ cm ^3$ find its diameter and the surface area.
→
How many terms are there in the series:

4, 7, 10, 13, ........,148?

→