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Recent questions tagged systemofequations
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1
Linear Algebra_25
Let AX=B be a system of n linear equations in n unknown with integer coefficient and the components of B are all integer. Consider the following (1)det(A)=1 (2)det(A)=0 (3)Solution X has integer entries (4)Solution X does not have all integer entries For the given system ... then 3 holds true (c)If 1, then 4 holds true (d)If 2, then 3 holds true I think (d) should be the answer.
asked
4 days
ago
in
Linear Algebra
by
Ayush Upadhyaya
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16.1k
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37
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linearalgebra
engineeringmathematics
systemofequations
0
votes
0
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2
System of Equations
My solution: Since the Determinant of matrix is Zero. So it will posses non trivial solution. Now what should be the answer ? According to me Option D as rank is < Order so infinite number of solutions
asked
Oct 25
in
Linear Algebra
by
Na462
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6.9k
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41
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linearalgebra
engineeringmathematics
systemofequations
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3
SELF DOUBT
consider a system of linear equation where AMxN XNx1 =BMx1 TRUE OR FALSE Q1 IF B=0 AND DETERMINENT OF A i.e A IS NOT EQUAL TO ZERO THEN IT MEANS UNIQUE SOLUTION?? Q2 IF B NOT EQUAL TO 0 AND DETERMINENT OF A i.e A IS NOT EQUAL TO ZERO THEN IT MEANS INFINITE MANY SOLUTION SOLUTION?? Q3 IF B IS NOT EQUAL TO 0 AND M<N THEN IT MEANS NO UNIQUE SOLUTION??
asked
Oct 3
in
Linear Algebra
by
eyeamgj
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5.8k
points)

20
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systemofequations
0
votes
1
answer
4
Linear Algebra RGPV 2001
Test the consistency of the following system of equations and solve if possible $3x + 3y +2z = 1$ $x + 2y = 4$ $10y + 3z = 2$ $2x  3y z = 5$
asked
Sep 29
in
Linear Algebra
by
Mk Utkarsh
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23.7k
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51
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linearalgebra
engineeringmathematics
systemofequations
0
votes
1
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5
Hk Dass Linear Algebra
Test the consistency of the following system of equations $5x + 3y + 7z = 4 $ $3x + 26y + 2z = 9$ $7x + 2y + 10z = 5$
asked
Sep 29
in
Linear Algebra
by
Mk Utkarsh
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(
23.7k
points)

42
views
linearalgebra
systemofequations
0
votes
1
answer
6
Linear system of equations
asked
Sep 16
in
Linear Algebra
by
Na462
Loyal
(
6.9k
points)

31
views
engineeringmathematics
linearalgebra
systemofequations
+2
votes
4
answers
7
ISI201604
If $a,b,c$ and $d$ satisfy the equations $$a+7b+3c+5d =16\\8a+4b+6c+2d = 16\\ 2a+6b+4c+8d = 16 \\ 5a+3b+7c+d= 16$$ Then $(a+d)(b+c)$ equals $4$ $0$ $16$ $16$
asked
Mar 31
in
Linear Algebra
by
jjayantamahata
Active
(
1.6k
points)

172
views
isi2016
engineeringmathematics
systemofequations
+1
vote
1
answer
8
GATE Linear Algebra
For what values of $\lambda$ the system of equations will have $2$ linear independent solutions  $x + y + z = 0$ $(\lambda + 1) y + (\lambda + 1) z = 0$ ($\lambda^{2} 1) z = 0$ Now the problem i'm facing is if there is ... rank of matrix will be $1$. Can anyone please explain in simple why the rank of matrix should be $1$ if we need $2$ Linear Independent solution. Thankyou.
asked
Mar 2
in
Linear Algebra
by
pilluverma123
(
323
points)

106
views
numericalanswers
linear
algebra
system
of
systemofequations
+1
vote
1
answer
9
Test Series ACE
How to solve? ________________ Number of nonnegative integer solutions such that x+y+z=17 where x>1,y>2,z>3 is 
asked
Jan 13
in
Linear Algebra
by
ankit_thawal
Active
(
2.1k
points)

92
views
systemofequations
0
votes
3
answers
10
Linear Homogeneous Equation (Allen 2017)
asked
Dec 1, 2017
in
Linear Algebra
by
stanchion
Junior
(
505
points)

106
views
system
of
systemofequations
nontrivialsolution
homogeneousequation
0
votes
3
answers
11
NUMBER of soutions the equations have?
Consider the following system system of equations x12x3=0 x1x2=0 2x12x2=0 No solution Infinite number of solutions Three solution unique solution
asked
Nov 10, 2017
in
Linear Algebra
by
Parshu gate
Active
(
5k
points)

75
views
engineeringmathematics
systemofequations
+23
votes
4
answers
12
GATE201713
Let $c_{1}.....c_{n}$ be scalars, not all zero, such that $\sum_{i=1}^{n}c_{i}a_{i}$ = 0 where $a_{i}$ are column vectors in $R^{n}$. Consider the set of linear equations $Ax = b$ where $A=\left [ a_{1}.....a_{n} \ ... of equations has a unique solution at $x=J_{n}$ where $J_{n}$ denotes a $n$dimensional vector of all 1. no solution infinitely many solutions finitely many solutions
asked
Feb 14, 2017
in
Linear Algebra
by
Arjun
Veteran
(
363k
points)

3.6k
views
gate20171
linearalgebra
systemofequations
normal
0
votes
2
answers
13
GATE2011GGGA6
The number of solutions for the following system of inequalities is $X_1≥ 0$ $X_2 ≥ 0$ $X_1+ X_2 ≤ 10$ $2X_1+ 2X_2 ≥ 22$ $0$ infinite $1$ $2$
asked
Feb 16, 2016
in
Numerical Ability
by
Akash Kanase
Boss
(
43k
points)

211
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gate2011_gg
numericalability
systemofequations
+26
votes
3
answers
14
GATE2016204
Consider the system, each consisting of $m$ linear equations in $n$ variables. If $m < n$, then all such systems have a solution. If $m > n$, then none of these systems has a solution. If $m = n$, then there exists a system which has a solution. Which ... following is CORRECT? $I, II$ and $III$ are true. Only $II$ and $III$ are true. Only $III$ is true. None of them is true.
asked
Feb 12, 2016
in
Linear Algebra
by
Akash Kanase
Boss
(
43k
points)

2.8k
views
gate20162
linearalgebra
systemofequations
normal
+1
vote
1
answer
15
TIFR2011MathsA13
$A$ is $3 \times 4$matrix of rank $3$. Then the system of equations, $Ax = b$ has exactly one solution.
asked
Dec 9, 2015
in
Linear Algebra
by
makhdoom ghaya
Boss
(
40.4k
points)

122
views
tifrmaths2011
linearalgebra
systemofequations
+2
votes
1
answer
16
TIFR2014A1
Consider the reactions $$X + 2Y \rightarrow 3Z\\2X + Z \rightarrow Y.$$ Let $n_{X}$, $n_{Y}$, $n_{Z}$ denote the numbers of molecules of chemicals $X, Y, Z$ in the reaction chamber. Then which of the following is conserved by both reactions? $n_{X} + n_{Y} + n_{Z}$. $n_{X}+ 7n_{Y} + 5n_{Z}$. $2n_{X} + 9n_{Y} − 3n_{Z}$. $3n_{X} − 3n_{Y} + 13n_{Z}$. None of the above.
asked
Nov 9, 2015
in
Linear Algebra
by
makhdoom ghaya
Boss
(
40.4k
points)

250
views
tifr2014
linearalgebra
systemofequations
+5
votes
1
answer
17
TIFR2010MathsB14
The equations. $x_{1}+2x_{2}+3x_{3}=1$ $x_{1}+4x_{2}+9x_{3}=1$ $x_{1}+8x_{2}+27x_{3}=1$ have Only one solution. Two solutions. Infinitely many solutions. No solutions
asked
Oct 15, 2015
in
Linear Algebra
by
makhdoom ghaya
Boss
(
40.4k
points)

261
views
tifrmaths2010
linearalgebra
systemofequations
+17
votes
4
answers
18
GATE2015333
If the following system has nontrivial solution, $px + qy + rz = 0$ $qx + ry + pz = 0$ $rx + py + qz = 0$, then which one of the following options is TRUE? $p  q + r = 0 \text{ or } p = q = r$ $p + q  r = 0 \text{ or } p = q = r$ $p + q + r = 0 \text{ or } p = q = r$ $p  q + r = 0 \text{ or } p = q = r$
asked
Feb 15, 2015
in
Linear Algebra
by
jothee
Veteran
(
106k
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2k
views
gate20153
linearalgebra
systemofequations
normal
+9
votes
3
answers
19
GATE2004IT6
What values of x, y and z satisfy the following system of linear equations? $$\begin{bmatrix} 1 &2 &3 \\ 1& 3 &4 \\ 2& 2 &3 \end{bmatrix} \begin{bmatrix} x\\y \\ z \end{bmatrix} = \begin{bmatrix} 6\\8 \\ 12 \end{bmatrix}$$ $x = 6$, $y = 3$, $z = 2$ $x = 12$, $y = 3$, $z =  4$ $x = 6$, $y = 6$, $z =  4$ $x = 12$, $y =  3$, $z = 0$
asked
Nov 2, 2014
in
Linear Algebra
by
Ishrat Jahan
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(
19.1k
points)

823
views
gate2004it
linearalgebra
systemofequations
easy
+20
votes
3
answers
20
GATE19961.7
Let $Ax = b$ be a system of linear equations where $A$ is an $m \times n$ matrix and $b$ is a $m \times 1$ column vector and $X$ is an $n \times1$ column vector of unknowns. Which of the following is false? The system has a solution if and only if, both $A$ ... a unique solution. The system will have only a trivial solution when $m=n$, $b$ is the zero vector and $\text{rank}(A) =n$.
asked
Oct 9, 2014
in
Linear Algebra
by
Kathleen
Veteran
(
59.6k
points)

1.9k
views
gate1996
linearalgebra
systemofequations
normal
+16
votes
5
answers
21
GATE201414
Consider the following system of equations: $3x + 2y = 1 $ $4x + 7z = 1 $ $x + y + z = 3$ $x  2y + 7z = 0$ The number of solutions for this system is ______________
asked
Sep 26, 2014
in
Linear Algebra
by
jothee
Veteran
(
106k
points)

2.3k
views
gate20141
linearalgebra
systemofequations
numericalanswers
normal
+1
vote
0
answers
22
GATE19989
Derive the expressions for the number of operations required to solve a system of linear equations in $n$ unknowns using the Gaussian Elimination Method. Assume that one operation refers to a multiplication followed by an addition.
asked
Sep 26, 2014
in
Linear Algebra
by
Kathleen
Veteran
(
59.6k
points)

199
views
gate1998
linearalgebra
systemofequations
descriptive
+12
votes
3
answers
23
GATE19981.2
Consider the following set of equations $$x+2y=5\\ 4x+8y=12\\ 3x+6y+3z=15$$ This set has unique solution has no solution has finite number of solutions has infinite number of solutions
asked
Sep 26, 2014
in
Linear Algebra
by
Kathleen
Veteran
(
59.6k
points)

1.2k
views
gate1998
linearalgebra
systemofequations
easy
+8
votes
2
answers
24
GATE200548
Consider the following system of linear equations : $$2x_1  x_2 + 3x_3 = 1$$ $$3x_1 + 2x_2 + 5x_3 = 2$$ $$x_1+4x_2+x_3 = 3$$ The system of equations has no solution a unique solution more than one but a finite number of solutions an infinite number of solutions
asked
Sep 21, 2014
in
Linear Algebra
by
gatecse
Boss
(
18.3k
points)

805
views
gate2005
linearalgebra
systemofequations
normal
+12
votes
4
answers
25
GATE200471
How many solutions does the following system of linear equations have? $x + 5y = 1$ $x  y = 2$ $x + 3y = 3$ infinitely many two distinct solutions unique none
asked
Sep 19, 2014
in
Linear Algebra
by
Kathleen
Veteran
(
59.6k
points)

1.2k
views
gate2004
linearalgebra
systemofequations
normal
+16
votes
2
answers
26
GATE200341
Consider the following system of linear equations $$\left( \begin{array}{ccc} 2 & 1 & 4 \\ 4 & 3 & 12 \\ 1 & 2 & 8 \end{array} \right) \left( \begin{array}{ccc} x \\ y \\ z \end{array} \right) = \left( \begin{array} ... are linearly dependent. For how many values of $\alpha$, does this system of equations have infinitely many solutions? \(0\) \(1\) \(2\) \(3\)
asked
Sep 17, 2014
in
Linear Algebra
by
Kathleen
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(
59.6k
points)

2.1k
views
gate2003
linearalgebra
systemofequations
normal
+15
votes
2
answers
27
GATE20083
The following system of equations $x_1 + x_2 + 2x_3 = 1$ $x_1 + 2x_2 + 3x_3 = 2$ $x_1 + 4x_2 + αx_3 = 4$ has a unique solution. The only possible value(s) for $α$ is/are $0$ either $0$ or $1$ one of $0, 1$, or $1$ any real number
asked
Sep 11, 2014
in
Linear Algebra
by
Kathleen
Veteran
(
59.6k
points)

1.8k
views
gate2008
easy
linearalgebra
systemofequations
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