Given that A= [ cc & & - ] and A^2=31, then - Vidyadip

Question

Given that $A=\left[\begin{array}{cc}\alpha & \beta \\ \gamma & -\alpha\end{array}\right]$ and $A^2=31$, then

✓

Answer

We have $, A=\left[\begin{array}{cc} \alpha & \beta \\ \gamma & -\alpha \end{array}\right] $
$\Rightarrow A^2=\left[\begin{array}{cc} \alpha & \beta \\ \gamma & -\alpha \end{array}\right]\left[\begin{array}{cc} \alpha & \beta \\ \gamma & -\alpha \end{array}\right]$
$=\left[\begin{array}{cc} \alpha^2+\beta \gamma & 0 \\
0 & \gamma \beta+\alpha^2 \end{array}\right]$
But $A^2=31$
$ \Rightarrow\left[\begin{array}{cc} \alpha^2+\beta \gamma & 0 \\ 0 & \alpha^2+\beta \gamma \end{array}\right]=\left[\begin{array}{ll} 3 & 0 \\ 0 & 3 \end{array}\right] $
$\Rightarrow \alpha^2+\beta \gamma=3$
$\Rightarrow 3-\alpha^2-\beta \gamma=0$

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 "M.C.Q (1 Marks)" from Matrices→Matrices — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the value of $\sec^2(\tan^{-1}2)+\text{cosec}^2(\cot^{-1}3)$

12
5
15
9

Find area bounded by curves $\{(\text{x},\text{y}):\text{y}\geq\text{x}^2\text{ andy}=\text{x}\}$ :

The general solution of differention eqution of the $e^x dy + (ye^x + 2x)dx = 0$ is :

The first step in formulating an LP problem is:

The determinant $\left|\begin{array}{ccc}y+k & y & y \\ y & y+k & y \\ y & y & y+k\end{array}\right|$ is equal to

A person travels 12km in the southward direction and then travels 5km to the right and then travels 15km toward the right and finally travels 5km towards the east, how far is he from his starting place?

5.5kms
3km
13km
6.4km

$Q^+$ denote the set of all positive rational numbers. If the binary operation $\text{a }\odot$ on $Q^+$ is defined as:
$\text{a }\odot=\frac{\text{ab}}{2}$, then the inverse of $3$ is:

The area bounded by the curve $y^2= 8x,$ the x-axis and the lastus rectum is:

Which of these is equal to $\int 2^{(x+3)} d x$, where $C$ is the constant of integration?

The xy-plane divided the line joining the point (-1, 3, 4) and (2, -5, 6)

Internally in the ratio 2 : 3
Externally in the ratio 2 : 3
Internally in the ratio 3 : 2
Externally in the ratio 3 : 2