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Recent questions tagged rankofmatrix
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Nullity of matrix
Nullity of a matrix = Total number columns – Rank of that matrix By how to calculate value of x when nullity is already given(1 in this case)
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Jan 24
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Linear Algebra
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Nandkishor3939
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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
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Jan 1
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Set Theory & Algebra
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Salazar
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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 $adj(B)$
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Oct 25, 2018
in
Linear Algebra
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Lakshman Patel RJIT
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73
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engineeringmathematics
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rankofmatrix
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Virtual Gate Test Series:Linear AlgebraRank Of The Matrix
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Oct 15, 2018
in
Linear Algebra
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Prince Sindhiya
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rankofmatrix
virtualgatetestseries
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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
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159
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151
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rankofmatrix
engineeringmathematics
matrix
+4
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4
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6
ISI201729
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 $1$ $3$ $1/2$ $1/3$
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Mar 29, 2018
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Linear Algebra
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jjayantamahata
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isi2017
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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. $n$
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Mar 4, 2018
in
Linear Algebra
by
Prince Sindhiya
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65
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engineeringmathematics
rankofmatrix
+5
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1
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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
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Lakshman Patel RJIT
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130
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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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37
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rankofmatrix
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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
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Manoja Rajalakshmi A
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69
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lineardependence
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11
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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131
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rankofmatrix
matrix
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engineeringmathematics
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1
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12
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
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331
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828
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matrix
rankofmatrix
matrices
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13
GF MT 4
Is the answer and explaination given correct ?
asked
Jan 7, 2017
in
Linear Algebra
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gatesjt
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937
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142
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gateforumtestseries
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ACEMockTest:Matrix algebraRank
asked
Dec 24, 2016
in
Linear Algebra
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KISHALAY DAS
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482
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matrix
rankofmatrix
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15
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
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pC
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159
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rankofmatrix
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