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Recent questions tagged rankofmatrix
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ISI2015MMA40
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 $3$
asked
Sep 23, 2019
in
Linear Algebra
by
Arjun
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isi2015mma
linearalgebra
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rankofmatrix
+2
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3
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2
ISI2018MMA12
The rank of the matrix $\begin{bmatrix} 1 &2 &3 &4 \\ 5& 6 & 7 & 8 \\ 6 & 8 & 10 & 12 \\ 151 & 262 & 373 & 484 \end{bmatrix}$ $1$ $2$ $3$ $4$
asked
May 11, 2019
in
Linear Algebra
by
akash.dinkar12
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42.4k
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129
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isi2018mma
engineeringmathematics
linearalgebra
rankofmatrix
+2
votes
1
answer
3
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)
asked
Jan 24, 2019
in
Linear Algebra
by
Nandkishor3939
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1.3k
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193
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engineeringmathematics
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matrices
rankofmatrix
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4
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
asked
Jan 1, 2019
in
Set Theory & Algebra
by
Salazar
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1.1k
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27
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matrices
rankofmatrix
discretemathematics
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1
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5
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 $adj(B)$
asked
Oct 25, 2018
in
Linear Algebra
by
Lakshman Patel RJIT
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58.8k
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126
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engineeringmathematics
linearalgebra
rankofmatrix
+1
vote
2
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6
Virtual Gate Test Series: Linear Algebra  Rank Of The Matrix
asked
Oct 15, 2018
in
Linear Algebra
by
Prince Sindhiya
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91
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engineeringmathematics
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rankofmatrix
virtualgatetestseries
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ISI2017MMA29
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 $1$ $3$ $1/2$ $1/3$
asked
Sep 15, 2018
in
Linear Algebra
by
jothee
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105k
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isi2017mma
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rankofmatrix
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0
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8
ISI2016MMA28
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($A$)
asked
Sep 13, 2018
in
Linear Algebra
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jothee
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105k
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isi2016mmamma
linearalgebra
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rankofmatrix
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1
answer
9
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.
asked
Jun 21, 2018
in
Mathematical Logic
by
bts
(
129
points)

246
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rankofmatrix
engineeringmathematics
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+7
votes
4
answers
10
ISI2017MMA29
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 $1$ $3$ $1/2$ $1/3$
asked
Mar 29, 2018
in
Linear Algebra
by
jjayantamahata
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1.5k
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539
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isi2017mma
engineeringmathematics
linearalgebra
rankofmatrix
+7
votes
3
answers
11
ISI2017MMA5
If $A$ is a $2 \times 2$ matrix such that trace $A = det \ A = 3,$ then what is the trace of $A^{1}$? $1$ $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{6}\right)$ $\left(\dfrac{1}{2}\right)$
asked
Mar 27, 2018
in
Linear Algebra
by
jjayantamahata
Active
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1.5k
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406
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isi2017mma
engineeringmathematics
linearalgebra
rankofmatrix
0
votes
1
answer
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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. $n1$ D. $n$
asked
Mar 4, 2018
in
Linear Algebra
by
Prince Sindhiya
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5.9k
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66
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engineeringmathematics
rankofmatrix
+5
votes
1
answer
13
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 $ $D)$ $n + r$
asked
Jan 22, 2018
in
Linear Algebra
by
Lakshman Patel RJIT
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58.8k
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212
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engineeringmathematics
linearalgebra
rankofmatrix
0
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0
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14
If we perform any row change or column change thn the rank of matrix change?
asked
Dec 25, 2017
in
Mathematical Logic
by
hem chandra joshi
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4.1k
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46
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rankofmatrix
0
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1
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15
virtual gate
If the rank of a (5 × 6) matrix Q is 4, then which one of the following statements is correct? (A) Q will have four linearly independent rows and four linearly independent columns (B) Q will have four linearly independent rows and five linearly independent columns (C) QQT will be invertible (D) QTQ will be invertible
asked
Nov 16, 2017
in
Linear Algebra
by
Manoja Rajalakshmi A
Boss
(
11.6k
points)

80
views
rankofmatrix
lineardependence
+2
votes
0
answers
16
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
asked
Nov 11, 2017
in
Linear Algebra
by
Parshu gate
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3.1k
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158
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rankofmatrix
matrices
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engineeringmathematics
+1
vote
1
answer
17
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.
asked
Jan 9, 2017
in
Linear Algebra
by
harshit agarwal
(
169
points)

889
views
matrices
rankofmatrix
linearalgebra
0
votes
0
answers
18
GF MT 4
Is the answer and explaination given correct ?
asked
Jan 7, 2017
in
Linear Algebra
by
gatesjt
Junior
(
905
points)

148
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gateforumtestseries
linearalgebra
rankofmatrix
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votes
2
answers
19
ACEMockTest:Matrix algebraRank
asked
Dec 24, 2016
in
Linear Algebra
by
KISHALAY DAS
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4.9k
points)

631
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matrices
rankofmatrix
0
votes
2
answers
20
Gate 2008 Ee
Answer given as option a ) My knowledge . Rank of a matrix Q is 4 implies 1 out of 5 rows of Q is zero linearly independent solution = nr n> no of unknowns r> rank therefore linerly independent solution = 54 = 1 What is linerly independent Rows ... ? linerly independent vectors ?
asked
May 3, 2016
in
Linear Algebra
by
pC
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(
21.5k
points)

171
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rankofmatrix
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