Let A be a 3 3 matrix of non-negative real elements such that A [… - Vidyadip

MCQ

Let $A$ be a $3 \times 3$ matrix of non-negative real elements such that $A\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]=3\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]$. Then the maximum value of $\operatorname{det}(\mathrm{A})$ is........................

A
$49$
B
$54$
✓
$27$
D
$50$

✓

Answer

Correct option: C.

$27$

c
$\begin{aligned} \text { Let } A & =\left[\begin{array}{lll}a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3\end{array}\right] \\ A\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right] & =3\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]\end{aligned}$

$ \Rightarrow a_1+a_2+a_3=3 $

$ \Rightarrow b_1+b_2+b_3=3 $

$ \Rightarrow c_1+c_2+c_3=3 $

Now,

$ |A|=\left(a_1 b_2 c_3+a_2 b_3 c_1+a_3 b_1 c_2\right) $

$ -\left(a_3 b_2 c_1+a_2 b_1 c_3+a_1 b_3 c_2\right)$

$\therefore$ From above in formation, clearly $|\mathrm{A}|_{\max }=27$, when $a_1=3, b_2=3, c_3=3$

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

The value of $\int_0^1 {\frac{{{x^4} + 1}}{{{x^2} + 1}}\,dx} $ is

Choose the correct answer from the given four options : The area of the region bounded by the ellipse $\frac{\text{x}^2}{25}+\frac{\text{y}^2}{16}=1$ is :

Let $*$ be a binary operation on $N$ defined by $a^ * b = a + b + 10$ for all $a, b \in N.$ The identity element for $*$ in $N$ is:

Let$\begin{vmatrix}\text{x}&2&\text{x}\\\text{x}^2&\text{x}&6\\\text{x}&\text{x}&6\end{vmatrix}=\text{ax}^4+\text{bx}^3+\text{cx}^2+\text{dx}+\text{e}.$ Then, the value of $5a + 4b + 3c + 2d + e$ is equal to:

Let $\lambda \in Z, \vec{a}=\lambda \hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=3 \hat{i}-\hat{j}+2 \hat{k}$. Let $\overrightarrow{ c }$ be a vector such that $(\vec{a}+\vec{b}+\vec{c}) \times \vec{c}=\overrightarrow{0}, \vec{a} \cdot \vec{c}=-17$ and $\vec{b} \cdot \vec{c}=-20$ Then $|\overrightarrow{ c } \times(\lambda \hat{i}+\hat{j}+\hat{ k })|^2$ is equal to

The area included between the parabolas $y^2 = 4x$ and $x^2 = 4y$ is $($in square units$)$

The latus rectum of the conic passing through the origin and having the property that normal at each point $(x, y)$ intersects the $x -$ axis at $((x + 1), 0)$ is :

If a dice is rolled two times, then what will be the probability of sum of appeared number is 7 ?

The value of $\int\frac{1}{\text{x}+\text{x}\log\text{x}}\text{ dx}$ is:

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