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

MCQ

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

A
$1+\alpha^2+\beta \gamma=0$
B
$1-\alpha^2-\beta \gamma=0$
C
$3-\alpha^2-\beta \gamma=0$
D
$3+\alpha^2+\beta \gamma=0$

✓

Answer

We have,
\[\begin{array}{l}
\text { 8. (c) : We have, } A=\left[\begin{array}{cc}
\alpha & \beta \\
\gamma & -\alpha
\end{array}\right] \\
\Rightarrow A^2=\left[\begin{array}{cc}
\alpha & \beta \\
\gamma & -\alpha
\end{array}\right]\left[\begin{array}{cc}
\alpha & \beta \\
\gamma & -\alpha
\end{array}\right]=\left[\begin{array}{cc}
\alpha^2+\beta \gamma & 0 \\
0 & \gamma \beta+\alpha^2
\end{array}\right]
\end{array}\]
But $A^2=31$
\[\begin{array}{l}
\Rightarrow\left[\begin{array}{cc}
\alpha^2+\beta \gamma & 0 \\
0 & \alpha^2+\beta \gamma
\end{array}\right]=\left[\begin{array}{ll}
3 & 0 \\
0 & 3
\end{array}\right] \\
\Rightarrow \alpha^2+\beta \gamma=3 \\
\Rightarrow 3-\alpha^2-\beta \gamma=0
\end{array}\]

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→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The angle between the two diagonals of a cube is:

Let $\overrightarrow{ a }$ be a non-zero vector parallel to the line of intersection of the two planes described by $\hat{i}+\hat{j}, \hat{i}+\hat{k}$ and $\hat{i}-\hat{j}, \hat{j}-\hat{k}$. If $\theta$ is the angle between the vector $\vec{a}$ and the vector $\vec{b}=2 \hat{i}-2 \hat{j}+\hat{k}$ and $\vec{a} \cdot \vec{b}=6$ then the ordered pair $(\theta,|\vec{a} \times \vec{b}|)$ is equal to

If $y^2(2-x)=x^3$, then $\left(\frac{d y}{d x}\right)_{(1,1)}$ is equal to

If $f(x) = {\sin ^2}x + {\sin ^2}\left( {x + \frac{\pi }{3}} \right) + \cos x\cos \left( {x + \frac{\pi }{3}} \right)$ and $g\left( {\frac{5}{4}} \right) = 1$, then $(gof)(x) = $

Which of the following functions from $\text{A}=\{\text{x}:-1\leq\text{x}\leq1\}$ to itself are bijections?

$\text{f(x)}=\frac{\text{x}}{2}$
$\text{g(x)}=\sin\big(\frac{\pi\text{x}}{2}\big)$
$\text{h(x)}=|\text{x}|$
$\text{k(x)}=\text{x}^2$

If $\text{P(A)}=\frac{3}{10},\text{P(B)}=\frac{2}{5}$ and $\text{P}(\text{A}\cap\text{B}=\frac{3}{5,}$ then P(A|B) + P(B|A) equals

$\frac{1}{4}$
$\frac{7}{12}$
$\frac{5}{12}$
$\frac{1}{3}$

Choose the correct answer from the given four options.
If A and B are two independent events with $\text{P}(\text{A})=\frac{3}{5}$ and $\text{P}(\text{A})=\frac{4}{9},$ then $\text{P}(\text{A'}\cap\text{B'})$ equals:

If $A , B$ are symmetric matrices of same order, then $AB - BA$ is _________ .

If $P=\left[\begin{array}{ll}1 & 0 \\ 1 / 2 & 1\end{array}\right]$, then $P^{50}$ is:

Let $f$ be a function such that $f(x)\, = \,\sum\limits_{n\, - \,1}^n {\left[ {r\, + \,\cos \frac{x}{r}} \right]} $ where [.] denotes greatest integer function and $x \in [0,\pi]$, then range of $f(x)$ is-