Download App

Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices4 Marks
Question
Let $A=\left[\begin{array}{cc}2 & 1 \\ 0 & -2\end{array}\right], B=\left[\begin{array}{cc}4 & 1 \\ -3 & -2\end{array}\right]$ and $C=\left[\begin{array}{ll}-3 & 2 \\ -1 & 4\end{array}\right]$. Find $A^2 + AC -5B$.
✓

Answer

Given : $A =\left[\begin{array}{cc}2 & 1 \\ 0 & -2\end{array}\right], B =\left[\begin{array}{cc}4 & 1 \\ -3 & -2\end{array}\right]$ and $C =\left[\begin{array}{ll}-3 & 2 \\ -1 & 4\end{array}\right]$
Now,
$ A^2=\left[\begin{array}{cc} 2 & 1 \\ 0 & -2 \end{array}\right]\left[\begin{array}{cc} 2 & 1 \\
0 & -2 \end{array}\right]=\left[\begin{array}{ll} 4+0 & 2-2 \\ 0+0 & 0+4 \end{array}\right]=\left[\begin{array}{ll}
4 & 0 \\ 0 & 4 \end{array}\right] $
$5 B=\left[\begin{array}{cc} 20 & 5 \\ -15 & -10 \end{array}\right]$
$A C=\left[\begin{array}{cc}2 & 1 \\ 0 & -2\end{array}\right]\left[\begin{array}{ll}-3 & 2 \\ -1 & 4\end{array}\right]=\left[\begin{array}{cc}-6-1 & 4+4 \\ 0+2 & 0-8\end{array}\right]=\left[\begin{array}{cc}-7 & 8 \\ 2 & -8\end{array}\right] $
$ \therefore A^2+A C-5 B=\left[\begin{array}{ll}4 & 0 \\ 0 & 4\end{array}\right]+\left[\begin{array}{cc}-7 & 8 \\ 2 & -8\end{array}\right]-\left[\begin{array}{cc}20 & 5 \\ -15 & -10\end{array}\right] $
$ =\left[\begin{array}{cc}4-7-20 & 0+8-5 \\ 0+2+15 & 4-8+10\end{array}\right] $
$ =\left[\begin{array}{cc}-23 & 3 \\ 17 & 6\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 value of a 'Honda' bike depreciated by $16\%$ in the first year and by $13\%$ in the second year. Find the value of the bike if it depreciated by $Rs.7,098$ in the second year.
→
If the speed of a car is increased by $10\ km$ per hr, it takes $18$ minutes less to cover a distance of $36\ km.$ Find the speed of the car.
→
Find the compounded ratio of the following:
$(m-n):(m+n), (m+n)^2 : (m^2+n^2) and (m^4 - n^4): (m^2-n^2) ^2$​​​​​​​
→
Find the curved surface area , the total surface area and the volume of a cone if its :
Height = 15 cm , radius = 8 cm
→
Ritu bought a saree for Rs. 60 x and sold it for Rs. (500 + 4x) at a loss of x%. Find the cost price.
→
Solve the following quadratic equation by factorisation method:
$\frac{x}{x+1}+\frac{x+1}{x}=\frac{34}{15} x \neq 0, x \neq-1$
→
Rupesh wanted to buy an air-conditioner. He bought it when the sales tax on it had just increased by 6%. As a result Rupesh had to pay Rs 1,920 more. Find the marked price of the air-conditioner.
→
If (a + 2 b + c), (a – c) and (a – 2 b + c) are in continued proportion, prove that b is the mean proportional between a and c.
→
If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus.
→
Solve the following quadratic equation:
$\frac{1}{a+b+x}=\frac{1}{a}+\frac{1}{b}+\frac{1}{x}, a+b \neq 0$
→