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Recent questions tagged systemofequations
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1
Self DoubtLA
In a nonhomogeneous equation Ax = b, x has a unique solution when $A^{1}$ exists i.e x = $A^{1}$b but when det(A) = 0 then we have infinite solution or many solution. please give a mathematical explanation of how the 2nd statement occurs?
asked
May 26
in
Mathematical Logic
by
MRINMOY_HALDER
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1.2k
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30
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linearalgebra
systemofequations
0
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1
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2
ISI2018MMA11
The value of $\lambda$ for which the system of linear equations $2xyz=12$, $x2y+z=4$ and $x+y+\lambda z=4$ has no solution is $2$ $2$ $3$ $3$
asked
May 11
in
Numerical Ability
by
akash.dinkar12
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40.4k
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51
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isi2018
engineeringmathematics
linearalgebra
systemofequations
0
votes
1
answer
3
ISI2019MMA14
If the system of equations $\begin{array} ax +y+z= 0 \\ x+by +z = 0 \\ x+y + cz = 0 \end{array}$ with $a,b,c \neq 1$ has a non trivial solutions, the value of $\frac{1}{1a} + \frac{1}{1b} + \frac{1}{1c}$ is $1$ $1$ $3$ $3$
asked
May 7
in
Linear Algebra
by
Sayan Bose
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6.9k
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113
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isi2019
linearalgebra
systemofequations
+1
vote
1
answer
4
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
Nov 15, 2018
in
Linear Algebra
by
Ayush Upadhyaya
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24.6k
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97
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linearalgebra
engineeringmathematics
systemofequations
0
votes
0
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5
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, 2018
in
Linear Algebra
by
Na462
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6.6k
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69
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linearalgebra
engineeringmathematics
systemofequations
+1
vote
0
answers
6
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, 2018
in
Linear Algebra
by
eyeamgj
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6k
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30
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systemofequations
0
votes
1
answer
7
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, 2018
in
Linear Algebra
by
Mk Utkarsh
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34.5k
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88
views
linearalgebra
engineeringmathematics
systemofequations
0
votes
1
answer
8
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, 2018
in
Linear Algebra
by
Mk Utkarsh
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34.5k
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94
views
linearalgebra
systemofequations
0
votes
1
answer
9
Linear system of equations
asked
Sep 16, 2018
in
Linear Algebra
by
Na462
Loyal
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6.6k
points)

62
views
engineeringmathematics
linearalgebra
systemofequations
0
votes
0
answers
10
ISI2017MMA18
Consider following system of equations: $\begin{bmatrix} 1 &2 &3 &4 \\ 5&6 &7 &8 \\ a&9 &b &10 \\ 6&8 &10 & 13 \end{bmatrix}$\begin{bmatrix} x1\\ x2\\ x3\\ x4 \end{bmatrix}$=$\begin{bmatrix} 0\\ 0\\ 0\\ 0 \ ... at least two distinct solution for ($x_{1},x_{2},x_{3},x_{4}$) is a parabola a straight line entire $\mathbb{R}^{2}$ a point
asked
Apr 25, 2018
in
Linear Algebra
by
Tesla!
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17.8k
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178
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isi2017
engineeringmathematics
linearalgebra
systemofequations
+3
votes
4
answers
11
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, 2018
in
Linear Algebra
by
jjayantamahata
Active
(
1.3k
points)

305
views
isi2016
engineeringmathematics
systemofequations
+1
vote
1
answer
12
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 $2$ ... 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, 2018
in
Linear Algebra
by
pilluverma123
(
317
points)

157
views
numericalanswers
linear
algebra
system
of
systemofequations
0
votes
1
answer
13
GATE20181GA7
Given that $a$ and $b$ are integers and $a+a^2 b^3$ is odd, which of the following statements is correct? $a$ and $b$ are both odd $a$ and $b$ are both even $a$ is even and $b$ is odd $a$ is odd and $b$ is even
asked
Feb 17, 2018
in
Numerical Ability
by
Arjun
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406k
points)

41
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gate2018me1
generalaptitude
numericalability
quadraticequations
systemofequations
+1
vote
1
answer
14
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, 2018
in
Linear Algebra
by
ankit_thawal
Active
(
1.4k
points)

109
views
systemofequations
+2
votes
1
answer
15
MadeEasy Test Series: General Aptitude  System Of Equations
how to solve such questions?
asked
Jan 5, 2018
in
Numerical Ability
by
charul
Junior
(
793
points)

189
views
madeeasytestseries
generalaptitude
systemofequations
0
votes
3
answers
16
Linear Homogeneous Equation (Allen 2017)
Consider a system of equations (λ – a)x + 2y +3z = 0, x +2(λ – b) y + 3z = 0, x + 2y + 3(λ – c) z = 0, which has a nontrivial solution. Product of all values of λ for above system is (1) abc + a + b + c + 2 (2) abc + a + b + c – 2 (3) abc – a – b – c – 2 (4) abc – a – b – c + 2 Ans given is Option C. Can anyone explain the complete solution?
asked
Dec 1, 2017
in
Linear Algebra
by
stanchion
Junior
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505
points)

132
views
system
of
systemofequations
nontrivialsolution
homogeneousequation
0
votes
3
answers
17
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
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(
3.1k
points)

98
views
engineeringmathematics
systemofequations
+29
votes
4
answers
18
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 $Ax = b$ ... 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
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406k
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5.1k
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gate20171
linearalgebra
systemofequations
normal
0
votes
2
answers
19
GATE2011 Aptitude Set 2: GA6
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
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(
41k
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264
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gate2011aptiset2
numericalability
systemofequations
+29
votes
3
answers
20
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 one of the ... 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
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(
41k
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3.9k
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gate20162
linearalgebra
systemofequations
normal
+1
vote
1
answer
21
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
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29.3k
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143
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tifrmaths2011
linearalgebra
systemofequations
+2
votes
1
answer
22
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
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29.3k
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283
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tifr2014
linearalgebra
systemofequations
+5
votes
1
answer
23
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
(
29.3k
points)

300
views
tifrmaths2010
linearalgebra
systemofequations
+20
votes
4
answers
24
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
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96.1k
points)

2.6k
views
gate20153
linearalgebra
systemofequations
normal
+10
votes
3
answers
25
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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16.3k
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1.1k
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gate2004it
linearalgebra
systemofequations
easy
+22
votes
3
answers
26
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 $n \times1$ ... has 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
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(
52k
points)

2.6k
views
gate1996
linearalgebra
systemofequations
normal
+17
votes
5
answers
27
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
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96.1k
points)

3.1k
views
gate20141
linearalgebra
systemofequations
numericalanswers
normal
+1
vote
1
answer
28
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
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(
52k
points)

258
views
gate1998
linearalgebra
systemofequations
gaussianelimination
descriptive
+14
votes
2
answers
29
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
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52k
points)

1.5k
views
gate1998
linearalgebra
systemofequations
easy
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