AP EAMCET · Maths · Matrices

The rank of the matrix $\left[\begin{array}{ccc}1 & 0 & 2 \\ 0 & 1 & -2 \\ 1 & -1 & 4 \\ 2 & 2 & 8\end{array}\right]$ is

A $2$
B $1$
C $3$
D $4$

Verified Solution

Answer & Solution

Correct Answer

(C) $3$

Step-by-step Solution

Detailed explanation

Let $A$…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

$\lim _{n \rightarrow \infty}\left[\frac{\sqrt{n^2-1^2}}{n^2}+\frac{\sqrt{n^2-2^2}}{n^2}+\frac{\sqrt{n^2-3^2}}{n^2}+\ldots\right.$ to $n$ terms $]=$

AP EAMCET 2017 Medium
A line has slope $m$ and $y$ -intercept 4. The distance between the origin and the line is equal to

AP EAMCET 2021 Easy
If $A$ is a matrix $\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right]$, then $A^n=\left[\begin{array}{ll}1 & 0 \\ n & 1\end{array}\right]$, $\forall n \in N$

AP EAMCET 2021 Medium
If $\int \frac{\sin ^2 \alpha-\sin ^2 x}{\cos x-\cos \alpha} d x=f(x)+A x+B$ and $B \in R$, then

AP EAMCET 2023 Easy
The points of intersection of the perpendicular tangents drawn to the ellipse $4 x^{2} + 9 y^{2} = 36$ lie on the curve

AP EAMCET 2018 Easy
$\text { If } \tan ^{-1} x+\tan ^{-1} y+\tan ^{-1} z=\frac{\pi}{2}$
then $1-x y-y z-z x$ is equal to

AP EAMCET 2010 Medium

Explore more questions on app

From AP EAMCET

If $\int \frac{d x}{e^x+4 e^{-x}} d x=f(x)+c$, then $f(x)$ is

AP EAMCET 2020 Medium
Among the following the correct statements are
I. $\mathrm{LiH}, \mathrm{BeH}_2$ and $\mathrm{MgH}_2$ are saline hydrides with significant covalent character
II. Saline hydrides are volatile
III. Electron - precise hydrides are Lewis bases
IV. The formula for chromium hydride is $\mathrm{CrH}$ The correct option is

AP EAMCET 2023 Easy
If the shortest distance from $(2,-14)$ to the circle $x^2+y^2+6 x+4 y-12=0$ is $d$ and the length of the tangent drawn from the same point to the circle is $l$, then $\sqrt{d+l}=$

AP EAMCET 2018 Easy
The wire of potentiometer has resistance $4 \Omega$ and length $1 \mathrm{~m}$. It is connected to a cell of emf $2 \mathrm{~V}$ and internal resistance $1 \Omega$. The current flowing through the potentiometer wire is

AP EAMCET 2020 Medium
The number of ways in which all the letters of the word COMBINATION can be arranged so that the vowels always come together is

AP EAMCET 2018 Medium
$\int_0^{\pi / 2} \frac{d x}{1+\tan ^3 x}$ is equal to :

AP EAMCET 2006 Easy

Explore more questions on app

The rank of the matrix \(\left[\begin{array}{ccc}1 & 0 & 2 \\ 0 & 1 & -2 \\ 1 & -1 & 4 \\ 2 & 2 & 8\end{array}\right]\) is

Answer & Solution

Step-by-step Solution

See the Complete Solution