If A= [ cc 2 & 1 -1 & 2 ], B= [ ll 1 & 0 1 & 1 ], C=ABA^ T and X … - Vidyadip

MCQ

If $A=\left[\begin{array}{cc}\sqrt{2} & 1 \\ -1 & \sqrt{2}\end{array}\right], B=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right], C=\mathrm{ABA}^{\mathrm{T}}$ and $\mathrm{X}$ $=\mathrm{A}^{\mathrm{T}} \mathrm{C}^2 \mathrm{~A}$, then $\operatorname{det} \mathrm{X}$ is equal to :

A
$243$
✓
$729$
C
$27$
D
$891$

✓

Answer

Correct option: B.

$729$

b
$\begin{aligned} & A=\left[\begin{array}{cc}\sqrt{2} & 1 \\ -1 & \sqrt{2}\end{array}\right] \Rightarrow \operatorname{det}(A)=3 \\ & B=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right] \Rightarrow \operatorname{det}(B)=1\end{aligned}$

Now $C=A B A^T \Rightarrow \operatorname{det}(C)=(\operatorname{dct}(A))^2 x \operatorname{det}(B)$

$|C|=9$

$\text { Now }|X|=\left|A^T C^2 A\right|$

$=\left|A^T\right||C|^2|A|$

$=|A|^2|C|^2$

$=9 \times 81$

$=729$

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 STD 12 - 3 and 4 . determinant and metrices→STD 12 - 3 and 4 . determinant and metrices — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Choose the correct answer from the given four options.
If $\tan^{-1}\text{x}+\tan^{-1}\text{y}=\frac{4\pi}{5},$ then $\cot^{-1}\text{x}+\cot^{-1}\text{y}$ equals to:

The differential equation $\text{x}\frac{\text{dy}}{\text{dx}}-\text{y}=\text{x}^{2}$ has the general solution:

A curve $y = f (x)$ passing through the point $\left( {1,\,\,\frac{1}{{\sqrt e }}} \right)$ satisfies the differential equation $\frac{{dy}}{{dx}} + x\,{e^{ - \;\frac{{{x^2}}}{2}}} =0.$ Then which of the following does not hold good?

If $\text{f(x)}=\text{a}|\sin\text{x}|+\text{be}^{|\text{x}|}+\text{c|x|}^3$and if f(x) is differentiable at x = 0, then:

Rolle's theorem is applicable in case of $\phi(\text{x})=\text{a}^{\sin\text{x}},\text{a}>\text{a}$ in :

The derivative of $x^{2 x}$ w.r.t. $x$ is

The value of objective function is maximum under linear constraints

Let $\bar{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}$ and $\vec{c}=\hat{j}-\hat{k}$ be three vectors such that $\vec{a} \times \vec{b}=\vec{c}$ and $\vec{a} \cdot \vec{b}=1$. If the length of projection vector of the vector $\vec{b}$ on the vector $\vec{a} \times \vec{c}$ is $l$, then the value of $3l^{2}$ is equal to $.....$

Let $a_n=\int_{-\pi}^\pi|x-1| \cos n x d x$ for all natural numbers $n$. Then, the sequence $\left(a_n\right)_{n \geq 0}$ satisfies

If $A, B, C$ are the angles of a triangle and $\left| {\begin{array}{*{20}{c}}1&1&1\\{1 + \sin A}&{1 + \sin B}&{1 + \sin C}\\{\sin A + {{\sin }^2}A}&{\sin B + {{\sin }^2}B}&{\sin C + {{\sin }^2}C} \end{array}} \right|$ $= 0$, then the triangle is