Download App

Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices3 Marks
Question
If $A=\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]$ and $I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ find $A^2 - 5A + 7 I.$
✓

Answer

$A^2=A \cdot A  $
$ =\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]  $
$ =\left[\begin{array}{cc}9-1 & 3+2 \\ -3-2 & -1+4\end{array}\right]  $
$ =\left[\begin{array}{cc}8 & 5 \\ -5 & 3\end{array}\right]  $
$ \Rightarrow A^2-5 A+71  $
$ =\left[\begin{array}{cc}8 & 5 \\ -5 & 3\end{array}\right]-5\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]+7\left[\begin{array}{cc}1 & 0 \\ 0 & 1\end{array}\right]  $
$ =\left[\begin{array}{cc}8 & 5 \\ -5 & 3\end{array}\right]-\left[\begin{array}{cc}15 & 5 \\ -5 & 10\end{array}\right]+\left[\begin{array}{ll}7 & 0 \\ 0 & 7\end{array}\right] $
$ =\left[\begin{array}{cc}-7 & 0 \\ 0 & -7\end{array}\right]+\left[\begin{array}{ll}7 & 0 \\ 0 & 7\end{array}\right]  $
$=\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right] $
$ =0 $

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

The sum of the ages of Vivek and his younger brother Amit is $47$ years. The product of their ages in years is $550$. Find their ages.
→
Find the 6th term from the end of the GP $8,4,2,1, \frac{1}{2} \ldots \frac{1}{1024}$.
→
All the three face cards of spades are removed from a well shuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probability of getting : a queen.
→
Solve the following equation by using formula :$\frac{x+1}{x+3}=\frac{3 x+2}{2 x+3}$
→
The total surface area of a right circular cone of slant height $13 \ cm$ is $90\pi \ cm^2.$ Calculate: its volume in $\ cm^3.$ Take $\pi = 3.14$
→
A cylinderical container with diameter of base $42\ cm$ contains sufficient water to submerge a rectangular soild of iron with dimesions $22\ cm \times 14\ cm \times 10.5\ cm.$ find the rise in level of the water the solid is submerged.
→
Find two consecutive positive even integers whose squares have the sum $340.$
→
If $sinA + cosA = m$ and $secA + cosecA = n$, prove that $n(m^2 - 1) = 2m$
→
If the mean of the following distribution is 22, then find the value of f.
Class0 - 1010 - 2020 - 3030 - 4040 - 50
Frequency12166f9
→
The following table givens the age of 50 student of a class . find the arithmetic mean of thier agges.
Age- Years 16-18 18-20 20-22 22-24 24-26
No.of students 2 7 21 17 3
→