Download App

Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices4 Marks
Question
Let $A =\left[\begin{array}{ll}1 & 0 \\ 2 & 1\end{array}\right], B =\left[\begin{array}{cc}2 & 3 \\ -1 & 0\end{array}\right]$. Find $A^2 + AB + B^2$.
✓

Answer

$A=\left[\begin{array}{ll}1 & 0 \\ 2 & 1\end{array}\right], $
$B=\left[\begin{array}{cc}2 & 3 \\ -1 & 0\end{array}\right] $
$ A^2=A \times A=\left[\begin{array}{ll}1 & 0 \\ 2 & 1\end{array}\right] \times\left[\begin{array}{ll}1 & 0 \\ 2 & 1\end{array}\right] $
$ =\left[\begin{array}{ll}1 \times 1+0 \times 2 & 1 \times 0+0 \times 1 \\ 2 \times 1+1 \times 2 & 2 \times 0+1 \times 1\end{array}\right] \\ =\left[\begin{array}{ll}1 & 0 \\ 4 & 1\end{array}\right]$
$B^2=B \times B=\left[\begin{array}{cc}2 & 3 \\ -1 & 0\end{array}\right] \times\left[\begin{array}{cc}2 & 3 \\ -1 & 0\end{array}\right] $
$ =\left[\begin{array}{cc}2 \times 2+3 \times-1 & 2 \times 3+3 \times 0 \\ -1 \times 2+0 \times-1 & -1 \times 3+0 \times 0\end{array}\right] $
$ =\left[\begin{array}{cc}1 & 6 \\ -2 & -3\end{array}\right] \\ \therefore A^2+A B+B^2$
$=\left[\begin{array}{ll}1 & 0 \\ 4 & 1\end{array}\right]+\left[\begin{array}{ll}2 & 3 \\ 3 & 6\end{array}\right]+\left[\begin{array}{cc}1 & 6 \\ -2 & -3\end{array}\right] $
$ =\left[\begin{array}{ll}4 & 9 \\ 5 & 4\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 "[4 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

The sum of three numbers in A.P.is $15$ the sum of the square of the exterme is $58.$ find the numbers.
→
Find the difference between the compound interest compounded yearly and half-yearly for the following:
Rs 20,000 for $1 \frac{1}{2}$ years at $16 \%$ p.a.
→
A farmer wishes to grow a $100\ m^2$ rectangular vegetable garden. Since he was with him only $30\ m$ barbed wire, he fences $3$ sides of the rectangular garden letting the compound of his house to act as the $4^{th}$ side. Find the dimensions of his garden .
→
The line through $A (−2, 3)$ and $B (4, b)$ is perpendicular to the line $2x – 4y = 5.$ Find the value
of $b.$
→
If $x=a \sec \alpha \cos \beta, y=b \sec \alpha \sin \beta$ and $z=c \tan \alpha$, then evaluate $\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}$.
→
Prove the following trigonometric identities.$\frac{1+\sin \theta}{\cos \theta}+\frac{\cos \theta}{1+\sin \theta}=2 \sec \theta$
→
Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.
$x^2+ 2 (m - 1) x + (m + 5) = 0.$
→
A manufacturer sells a microwave with a marked price of $Rs\ 11,000$ to the distributor for $Rs\ 7,500$. The distributor sells it to the retailer at a profit of $Rs\ 1,500$. The retailer sells to the customer at the marked price. If tax is charged at $8\%,$ find the $\text{VAT}$ paid by the retailer and the price paid by the customer.
→
In Δ ABC, B and Care fixed points. Find the locus of point A which moves such that the area of Δ ABC remains the same. 
→

The angles of depression of two cars on a straight road as observed from the top of a 42m high building are 60° and 75° respectively. Find the distance between the cars if they are on opposite sides of the building. 

→