AP EAMCET · Maths · Matrices
In a matrix \(A\), if all the sub matrices or \(k\) orcer are singular and there is one non-singular sub matrix of order r \((r < k)\), then the rank \((\rho)\) of the matrix A
- A satisfies \(r \leq \rho < k\)
- B is equal to \(r\)
- C is equal to \((\mathrm{k}-1)\)
- D is equal to \((\mathrm{k}+1)\)
Answer & Solution
Correct Answer
(A) satisfies \(r \leq \rho < k\)
Step-by-step Solution
Detailed explanation
Since, all the sub-matrices of \(k^{\text {th }}\) order are singular. \(\therefore \quad\) Rank of \(A=\rho < k\) \(\Rightarrow \rho < k\) ...(i) Also, there is one non-singular sub matrix of order \(r\). So, \(r \leq\) Rank of \(A\) \(\Rightarrow r \leq \rho\) ...(ii) From…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(g(x)=1+x-[x]\) and \(f(x)= \begin{cases}-1, & x < 0 \\ 0, & x=0 \\ 1, & x>0\end{cases}\) \([x]\) denotes the greatest integer less than or equal to \(x\). Then for all \(\mathrm{x}, \mathrm{f}(\mathrm{g}(\mathrm{x}))=\)AP EAMCET 2025 Medium
- \(\int \frac{\operatorname{cosec}^2 x-2022}{\cos ^{2022} x} d x=f(x)+C \Rightarrow f(\pi / 4)=\)AP EAMCET 2022 Easy
- \(\int_{-3}^3|2-x| d x=\)AP EAMCET 2024 Easy
- If the latus rectum of an ellipse is equal to half of minor axis, then its eccentricity isAP EAMCET 2022 Easy
- If \(\bar{a}=\bar{i}+4 \bar{j}-4 \bar{k}, \bar{b}=-2 \bar{i}+5 \bar{j}-2 \bar{k}\) and \(\bar{c}=3 \bar{i}-2 \bar{j}-4 \bar{k}\) are three vectors such that \((\bar{b} \times \bar{c}) \times \bar{a}=x \bar{i}+y \bar{j}+z \bar{k}\) then \(x+y-z=\)AP EAMCET 2025 Medium
- In \(\triangle A B C\), if \(a, b, c\) are 5,12 and 13 respectively, then \(b^2 \sin 2 C+c^2 \sin 2 B=\)AP EAMCET 2023 Medium
More PYQs from AP EAMCET
- Match the following
The correct answer isList-I (Reaction) List-II (Catalyst) A) Hydrogenation of vegetable oils I. Ni B) Decomposition of potassium chlorate II. \(\mathrm{MnO}_2\) C) Oxidation of \(\mathrm{SO}_2\) in lead chamber process III. Pt D) Oxidation of ammonia in Ostwald's process IV. \(\mathrm{NO}(\mathrm{g})\) AP EAMCET 2025 Easy - \(\sin 120^{\circ} \cos 150^{\circ}-\cos 240^{\circ} \sin 330^{\circ}\) is equal to :AP EAMCET 2006 Easy
- The correct order of increasing acidic strength among the following isAP EAMCET 2020 Medium
- If the lines \(x^2+2 x y-35 y^2-4 x+44 y-12=0\) and \(5 x+k y-8=0\) are concurrent, then \(k\) equalsAP EAMCET 2021 Medium
- If the probability function of a random variable \(\mathrm{X}\) is given by \(P(\mathrm{X}=k)=\frac{3^{c k}}{k !}\) for \(k=1,2,3, \ldots\) (where \(c\) is a constant), then \(c=\)AP EAMCET 2017 Easy
- The kinetic energy of a particle moving along a straight line is proportional to the time ' \(t\) ' of its travel. Then its acceleration is proportional toAP EAMCET 2017 Easy