Let A be a symmetric matrix such that |A|=2 and [ ll 2 & 1 3 & 3 … - Vidyadip

MCQ

Let $A$ be a symmetric matrix such that $|A|=2$ and $\left[\begin{array}{ll}2 & 1 \\ 3 & \frac{3}{2}\end{array}\right] A =\left[\begin{array}{ll}1 & 2 \\ \alpha & \beta\end{array}\right]$. If the sum of the diagonal elements of $A$ is s, then $\frac{\beta s}{\alpha^2}$ is equal to $..........$.

✓
$5$
B
$6$
C
$7$
D
$8$

✓

Answer

Correct option: A.

$5$

a
$\left[\begin{array}{ll}2 & 1 \\3 & \frac{3}{2}\end{array}\right]\left[\begin{array}{ll} a & b \\b & c\end{array}\right]=\left[\begin{array}{ll}1 & 2 \\\alpha & \beta\end{array}\right]$

Now $a c-b^2=2$ and $2 a+b=1$ and $2 b + c =2$

solving all these above equations we get

$\frac{1-b}{2} \times\left(\frac{2-2 b}{1}\right)-b^2=2$

$\Rightarrow(1-b)^2-b^2=2$

$\Rightarrow 1-2 b=2$

$\Rightarrow b=-\frac{1}{2} \text { and } a=\frac{3}{4} \text { and } c=3$

Hence $\alpha=3 a+\frac{3 b}{2}=\frac{9}{4}-\frac{3}{4}=\frac{3}{2}$

and $\beta=3 b+\frac{3 c}{2}=-\frac{3}{2}+\frac{9}{2}=3$

also $s = a + c =\frac{15}{4}$

$\therefore \frac{\beta s}{\alpha^2}=\frac{3 \times 15}{4 \times \frac{9}{4}}=5$

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 3 and 4 . determinant and metrices→3 and 4 . determinant and metrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The equation of the plane passing through (2, −3, 1) and is normal to the line joining the points (3, 4, −1) and (2, −1, 5) is given by:

If $\alpha \neq \mathrm{a}, \beta \neq \mathrm{b}, \gamma \neq \mathrm{c}$ and $\left|\begin{array}{lll}\alpha & \mathrm{b} & \mathrm{c} \\ \mathrm{a} & \beta & \mathrm{c} \\ \mathrm{a} & \mathrm{b} & \gamma\end{array}\right|=0$,then $\frac{a}{\alpha-a}+\frac{b}{\beta-b}+\frac{\gamma}{\gamma-c}$ is equal to :

If $P(A)=0.4, P(B)=0.8$ and $P(B \mid A)=0.6$, then $P(A \cup B)$ is equal to

The value of $\int_{\, - 2}^{\,2} {\left[ {p\ln \left( {\frac{{1 + x}}{{1 - x}}} \right) + q\ln {{\left( {\frac{{1 - x}}{{1 + x}}} \right)}^{ - 2}} + r} \right]\,dx} $ depends on

$\int\frac{\text{x}^3}{\text{x}+1}\text{ dx}$ is equal to:

$\text{x}+\frac{\text{x}^2}{2}+\frac{\text{x}^3}{3}-\log|1-\text{x}|+\text{C}$
$\text{x}+\frac{\text{x}^2}{2}-\frac{\text{x}^3}{3}-\log|1-\text{x}|+\text{C}$
$\text{x}-\frac{\text{x}^2}{2}-\frac{\text{x}^3}{3}-\log|1-\text{x}|+\text{C}$
$\text{x}-\frac{\text{x}^2}{2}+\frac{\text{x}^3}{3}-\log|1-\text{x}|+\text{C}$

The area of the shorter region bounded by $|y| = 4\, -\, x^2$ and $|y| = 3x$ is given by $\left( {3K + \frac{1}{3}} \right)$ sq-unit where $K$ is equal to

If $\begin{bmatrix}2\text{x}+\text{y}&4\text{x}\\5\text{x}-7&4\text{x}\end{bmatrix}=\begin{bmatrix}7&7\text{y}-13\\\text{y}&\text{x}+6\end{bmatrix},$ then the value of x and y is:

x = 3, y = 1
x = 2, y = 3
x = 2, y = 4
x = 3, y = 3

Area of the region bounded by the curve $y=\cos x$, $x=\frac{\pi}{2}$ and $x=\frac{3 \pi}{2}$ is __________ sq. units.

Let $[x]$ denote the largest integer not exceeding $x$ and $\{x\}=x-[x]$. Then, $\int \limits_0^{2012} \frac{e^{\cos (\pi\{x\})}}{e^{\cos (\pi\{x\})}+e^{-\cos (\pi\{x\})}} d x$ is equal to

A bag contains 10 white and 6 black balls. 4 balls are successively drawn out without replacement. What is the probability that they are alternately of different colours?