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Recent questions tagged rank-of-matrix
2
votes
2
answers
1
Made Easy: Linear Algebra (MSQ)
Let $A$ be a $3$ x $3$ matrix with rank $2$. Then, $AX=0$ has The trivial solution $X=0$. One independent solution. Two independent solution. Three independent solution.
DebSujit
asked
in
Linear Algebra
Sep 19
by
DebSujit
265
views
linear-algebra
engineering-mathematics
rank-of-matrix
matrix
system-of-equations
1
vote
1
answer
2
TIFR CSE 2022 | Part B | Question: 14
Let $G$ be a directed graph (with no self-loops or parallel edges) with $n \geq 2$ vertices and $m$ edges. Consider the $n \times m$ incidence matrix $M$ of $G$, whose rows are indexed by the vertices of $G$ and the columns by the edges of $G$ ... . Then, what is the rank of $M?$ $m-1$ $m-n+1$ $\lceil m / 2\rceil$ $n-1$ $\lceil n / 2\rceil$
admin
asked
in
Graph Theory
Sep 1
by
admin
58
views
tifr2022
graph-theory
graph-connectivity
rank-of-matrix
13
votes
1
answer
3
TIFR CSE 2022 | Part A | Question: 8
Let $A$ be the $(n+1) \times(n+1)$ matrix given below, where $n \geq 1$. For $i \leq n$, the $i$-th row of $A$ has every entry equal to $2i-1$ and the last row, i.e., the $(n+1)$-th row of $A$ has every entry equal to $-n^2$ ... $A$ has rank $n$ $A^2$ has rank $1$ All the eigenvalues of $A$ are distinct All the eigenvalues of $A$ are $0$ None of the above
Lakshman Patel RJIT
asked
in
Linear Algebra
Sep 1
by
Lakshman Patel RJIT
223
views
tifr2022
linear-algebra
rank-of-matrix
eigen-value
2
votes
1
answer
4
TIFR CSE 2021 | Part A | Question: 3
Let $M$ be an $n \times m$ real matrix. Consider the following: Let $k_{1}$ be the smallest number such that $M$ can be factorized as $A \cdot B$, where $A$ is an $n \times k_{1}$ and $B$ is a $k_{1} \times m$ matrix. Let $k_{2}$ be the smallest number ... $k_{1}= k_{2}= k_{3}$ No general relationship exists among $k_{1}, k_{2}$ and $k_{3}$
soujanyareddy13
asked
in
Linear Algebra
Mar 25, 2021
by
soujanyareddy13
353
views
tifr2021
linear-algebra
matrix
rank-of-matrix
20
votes
6
answers
5
GATE CSE 2021 Set 2 | Question: 24
Suppose that $P$ is a $4 \times 5$ matrix such that every solution of the equation $\text{Px=0}$ is a scalar multiple of $\begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T$. The rank of $P$ is __________
Arjun
asked
in
Linear Algebra
Feb 18, 2021
by
Arjun
8.0k
views
gatecse-2021-set2
numerical-answers
linear-algebra
matrix
rank-of-matrix
2
votes
1
answer
6
TIFR CSE 2020 | Part A | Question: 2
Let $M$ be a real $n\times n$ matrix such that for$ every$ non-zero vector $x\in \mathbb{R}^{n},$ we have $x^{T}M x> 0.$ Then Such an $M$ cannot exist Such $Ms$ exist and their rank is always $n$ Such $Ms$ exist, but their eigenvalues are always real No eigenvalue of any such $M$ can be real None of the above
Lakshman Patel RJIT
asked
in
Linear Algebra
Feb 10, 2020
by
Lakshman Patel RJIT
988
views
tifr2020
engineering-mathematics
linear-algebra
rank-of-matrix
eigen-value
0
votes
0
answers
7
ISI2015-MMA-40
Let $x_1, x_2, x_3, x_4, y_1, y_2, y_3$ and $y_4$ be fixed real numbers, not all of them equal to zero. Define a $4 \times 4$ matrix $\textbf{A}$ ... $(\textbf{A})$ equals $1$ or $2$ $0$ $4$ $2$ or $3$
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
422
views
isi2015-mma
linear-algebra
matrix
rank-of-matrix
2
votes
3
answers
8
ISI2018-MMA-12
The rank of the matrix $\begin{bmatrix} 1 &2 &3 &4 \\ 5& 6 & 7 & 8 \\ 6 & 8 & 10 & 12 \\ 151 & 262 & 373 & 484 \end{bmatrix}$ $1$ $2$ $3$ $4$
akash.dinkar12
asked
in
Linear Algebra
May 11, 2019
by
akash.dinkar12
1.1k
views
isi2018-mma
engineering-mathematics
linear-algebra
rank-of-matrix
4
votes
1
answer
9
Nullity of matrix
Nullity of a matrix = Total number columns – Rank of that matrix But how to calculate value of x when nullity is already given(1 in this case)
Nandkishor3939
asked
in
Linear Algebra
Jan 24, 2019
by
Nandkishor3939
2.3k
views
engineering-mathematics
linear-algebra
matrix
rank-of-matrix
0
votes
0
answers
10
Wiki example - Rouché–Capelli_theorem
What is the rank of the augmented matrix and coefficient matrix here ? x + y + 2z = 3, x + y + z = 1, 2x + 2y + 2z = 2 The example says it’s Augmented Matrix Rank is 3 and Coefficent Matrix Rank is 2, Can someone share the solution using echelon Form? This is a question from wiki page example here
Salazar
asked
in
Set Theory & Algebra
Jan 1, 2019
by
Salazar
133
views
matrix
rank-of-matrix
discrete-mathematics
0
votes
1
answer
11
Rank of the matrix
Given that a matrix $[A]_{4\times4},$any one row/column is dependent on the others, and given matrix are singular matrix$(|A|=0)$. And another matrix $B=adj(A),$then find them, $1)$Rank of the matrix $B$ $2)$Rank of the marix $adj(B)$
Lakshman Patel RJIT
asked
in
Linear Algebra
Oct 25, 2018
by
Lakshman Patel RJIT
1.3k
views
engineering-mathematics
linear-algebra
rank-of-matrix
3
votes
2
answers
12
Virtual Gate Test Series: Linear Algebra - Rank Of The Matrix
Prince Sindhiya
asked
in
Linear Algebra
Oct 15, 2018
by
Prince Sindhiya
929
views
engineering-mathematics
linear-algebra
matrix
rank-of-matrix
virtual-gate-test-series
0
votes
0
answers
13
ISI2017-MMA-29
Suppose the rank of the matrix $\begin{pmatrix} 1 & 1 & 2 & 2 \\ 1 & 1 & 1 & 3 \\ a & b & b & 1 \end{pmatrix}$ is 2 for some real numbers $a$ and $b$. Then the $b$ equals $1$ $3$ $1/2$ $1/3$
go_editor
asked
in
Linear Algebra
Sep 15, 2018
by
go_editor
673
views
isi2017-mma
engineering-mathematics
linear-algebra
rank-of-matrix
1
vote
1
answer
14
ISI2016-MMA-28
Let $A$ be a square matrix such that $A^3 =0$, but $A^2 \neq 0$. Then which of the following statements is not necessarily true? $A \neq A^2$ Eigenvalues of $A^2$ are all zero rank($A$) > rank($A^2$) rank($A$) > trace($A$)
go_editor
asked
in
Linear Algebra
Sep 13, 2018
by
go_editor
248
views
isi2016-mmamma
linear-algebra
matrix
eigen-value
rank-of-matrix
0
votes
1
answer
15
Rank of a matrix
Let A be a 4×3 real matrix with rank 2. Let B be transpose matrix of A. Which one of the following statement is TRUE? (a) Rank of BA is less than 2. (b) Rank of BA is equal to 2. (c) Rank of BA is greater than 2. (d) Rank of BA can be any number between 1 and 3.
bts
asked
in
Mathematical Logic
Jun 21, 2018
by
bts
1.5k
views
rank-of-matrix
engineering-mathematics
matrix
9
votes
8
answers
16
ISI2017-MMA-29
Suppose the rank of the matrix $\begin{pmatrix}1&1&2&2\\1&1&1&3\\a&b&b&1\end{pmatrix}$ is $2$ for some real numbers $a$ and $b$. Then $b$ equals $1$ $3$ $1/2$ $1/3$
jjayantamahata
asked
in
Linear Algebra
Mar 29, 2018
by
jjayantamahata
1.8k
views
isi2017-mma
engineering-mathematics
linear-algebra
rank-of-matrix
8
votes
3
answers
17
ISI2017-MMA-5
If $A$ is a $2 \times 2$ matrix such that trace $A = det \ A = 3,$ then what is the trace of $A^{-1}$? $1$ $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{6}\right)$ $\left(\dfrac{1}{2}\right)$
jjayantamahata
asked
in
Linear Algebra
Mar 27, 2018
by
jjayantamahata
1.4k
views
isi2017-mma
engineering-mathematics
linear-algebra
rank-of-matrix
0
votes
1
answer
18
IE Gate 2007
Let $A$ = $[a_{ij}]$, $1{\leq}i$, $j{\leq}n$, with $n{\geq}3$ and $a_{ij}$ = $i.j$. Then the rank of $A$ is A. $0$ B. $1$ C. $n-1$ D. $n$
Prince Sindhiya
asked
in
Linear Algebra
Mar 4, 2018
by
Prince Sindhiya
298
views
engineering-mathematics
rank-of-matrix
6
votes
1
answer
19
Made easy books GATE - 2015( IN ) 1 mark
Let $A$ be a $n\times n$ matrix with rank $ r ( 0 < r < n ) .$Then $AX = 0$ has $p$ independent solutions,where $p$ is $A)$ $r$ $B)$ $n$ $C)$ $n - r $ $D)$ $n + r$
Lakshman Patel RJIT
asked
in
Linear Algebra
Jan 22, 2018
by
Lakshman Patel RJIT
1.8k
views
engineering-mathematics
linear-algebra
rank-of-matrix
0
votes
0
answers
20
If we perform any row change or column change thn the rank of matrix change?
hem chandra joshi
asked
in
Mathematical Logic
Dec 25, 2017
by
hem chandra joshi
131
views
rank-of-matrix
3
votes
0
answers
21
rank of matrix
The rank of the matrix of coefficients of a homogeneous system of m linear equations in n unknowns is never less than the rank of the augmented matrix. (A) Always true (B) Sometimes true (C) False (D) None of the above
Parshu gate
asked
in
Linear Algebra
Nov 11, 2017
by
Parshu gate
421
views
rank-of-matrix
matrix
linear-algebra
engineering-mathematics
2
votes
1
answer
22
Rank of matrix
The rank of above matrix is 3 then what is that square sub matrix of order 3 whose determinant is not equal to 0.
harshit agarwal
asked
in
Linear Algebra
Jan 9, 2017
by
harshit agarwal
1.4k
views
matrix
rank-of-matrix
linear-algebra
1
vote
1
answer
23
GF MT 4
Is the answer and explaination given correct ?
gatesjt
asked
in
Linear Algebra
Jan 7, 2017
by
gatesjt
537
views
gateforum-test-series
linear-algebra
rank-of-matrix
0
votes
2
answers
24
ACE-MockTest:Matrix algebra-Rank
KISHALAY DAS
asked
in
Linear Algebra
Dec 24, 2016
by
KISHALAY DAS
3.1k
views
matrix
rank-of-matrix
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