Let 0 and A= [ ccc & & 3 & & - & & 2 ]. If B= [ ccc 3 & -9 & 3 - … - Vidyadip

MCQ

Let $\alpha \beta \neq 0$ and $A=\left[\begin{array}{ccc}\beta & \alpha & 3 \\ \alpha & \alpha & \beta \\ -\beta & \alpha & 2 \alpha\end{array}\right]$. If $B=\left[\begin{array}{ccc}3 \alpha & -9 & 3 \alpha \\ -\alpha & 7 & -2 \alpha \\ -2 \alpha & 5 & -2 \beta\end{array}\right]$ is the matrix of cofactors of the elements of $A$, then $\operatorname{det}(A B)$ is equal to.

A
$343$
B
$125$
C
$64$
✓
$216$

✓

Answer

Correct option: D.

$216$

d
Equating co-factor fo $\mathrm{A}_{21}$

$ \left(2 \alpha^2-3 \alpha\right)=\alpha $

$ \alpha=0,2 \text { (accept) }$

Now, $2 \alpha^2-\alpha \beta=3 \alpha$

$ \alpha=2 \quad \beta=1 $

$ |A B|=|A \operatorname{cof}(A)|=|A|^3$

$A=\left|\begin{array}{ccc}1 & 2 & 3 \\ 2 & 2 & 1 \\ -1 & 2 & 4\end{array}\right|=6-2(9)+3(6)=6$

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

Which of the following statement is correct?

Let $f:[0,1] \rightarrow R$ (the set of all real numbers) be a function. Suppose the function $f$ is twice differentiable, $f(0)=f(1)=0$ and satisfies $f^{\prime \prime}(x)-2 f^{\prime}(x)+f(x) \geq e^x, x \in[0,1]$

$1.$ Which of the following is true for $0 < x < 1$ ?

$(A)$ $0 < $ f(x) $ < \infty$

$(B)$ $-\frac{1}{2} < f(x) < \frac{1}{2}$

$(C)$ $-\frac{1}{4} < f(x) < 1$

$(D)$ $-\infty < $ f $($ x $) < 0$

$2.$ If the function $e^{-x} f(x)$ assumes its minimum in the interval $[0,1]$ at $x=\frac{1}{4}$, which of the following is true?

$(A)$ $f^{\prime}(x)$

$(B)$ $f^{\prime}(x)>f(x), 0$

$(C)$ f $^{\prime}(x)$

$(D)$ $f^{\prime}(x)$

Give the answer question $1$ and $2.$

The function f(x) = [x], where [x] denotes the greatest integer function, is continuous at:

4
-2
1
1.5

Set $A$ has $3$ elements and set $B$ has $4$ elements. The number of injection that can be defined from $A$ to $B$ is

Let $\vec{a}$ and $\vec{b}$ are non-collinear. If $\vec{c}=(x-2) \vec{a}+\vec{b}$ and $\vec{d}=(2 x+1) \vec{a}-\vec{b}$ are collinear, then find the value of $x$.

The integral $\int_{\pi /6}^{\pi /4} {\frac{{dx}}{{\sin \,2x\,\left( {{{\tan }^5}\,x + {{\cot }^5}\,x} \right)}}} $ equals

The area bounded by the curve $x=3 y^2-9$ and the line $x=0, y=0$ and $y=1$ is

Let f be an injective map with domain {x, y, z} and range {1, 2, 3}, such that exactly one of the following statements is correct and the remaining are false.

$\text{f(x)}=1,\ \text{f(y)}\neq1,\ \text{f(z)}\neq2.$

The value of f^-1(1)is:

x
y
z
None of these.

Choose the correct answer:
Smaller area enclosed by the circle x² + y² = 4 and the line x + y = 2 is:

$2(\pi-2)$
$\pi-2$
$2\pi-1$
$2(\pi+2).$

Integrating factor of differential equation $\frac{d y}{d x}+y \tan x-\sec x=0$ is