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Recent questions tagged system-of-equations
0
votes
3
answers
61
ISI2015-MMA-44
Let $P_1$, $P_2$ and $P_3$ denote, respectively, the planes defined by $\begin{array} {} a_1x +b_1y+c_1z=\alpha _1 \\ a_2x +b_2y+c_2z=\alpha _2 \\ a_3x +b_3y+c_3z=\alpha _3 \end{array}$ It is given that $P_1$, $P_2$ and $P_3$ ... then the planes do not have any common point of intersection intersect at a unique point intersect along a straight line intersect along a plane
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
924
views
isi2015-mma
linear-algebra
system-of-equations
1
vote
1
answer
62
ISI2015-DCG-11
Let two systems of linear equations be defined as follows: $\begin{array} {} & x+y & =1 \\ P: & 3x+3y & =3 \\ & 5x+5y & =5 \end{array}$ ... $P$ and $Q$ are inconsistent $P$ and $Q$ are consistent $P$ is consistent but $Q$ is inconsistent None of the above
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
429
views
isi2015-dcg
linear-algebra
system-of-equations
1
vote
1
answer
63
ISI2016-DCG-11
Let two systems of linear equations be defined as follows: $\begin{array}{lll} & x+y & =1 \\ P: & 3x+3y & =3 \\ & 5x+5y & =5 \end{array}$ ... $P$ and $Q$ are inconsistent $P$ and $Q$ are consistent $P$ is consistent but $Q$ is inconsistent None of the above
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
460
views
isi2016-dcg
linear-algebra
system-of-equations
0
votes
1
answer
64
Self Doubt-LA
In a non-homogeneous 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?
mrinmoyh
asked
in
Mathematical Logic
May 26, 2019
by
mrinmoyh
461
views
linear-algebra
system-of-equations
1
vote
1
answer
65
ISI2018-MMA-11
The value of $\lambda$ for which the system of linear equations $2x-y-z=12$, $x-2y+z=-4$ and $x+y+\lambda z=4$ has no solution is $2$ $-2$ $3$ $-3$
akash.dinkar12
asked
in
Quantitative Aptitude
May 11, 2019
by
akash.dinkar12
856
views
isi2018-mma
engineering-mathematics
linear-algebra
system-of-equations
2
votes
1
answer
66
ISI2019-MMA-14
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 $\frac{1}{1-a} + \frac{1}{1-b} + \frac{1}{1-c}$ is $1$ $-1$ $3$ $-3$
Sayan Bose
asked
in
Linear Algebra
May 6, 2019
by
Sayan Bose
943
views
isi2019-mma
linear-algebra
system-of-equations
2
votes
2
answers
67
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.
Ayush Upadhyaya
asked
in
Linear Algebra
Nov 15, 2018
by
Ayush Upadhyaya
2.0k
views
linear-algebra
engineering-mathematics
system-of-equations
1
vote
0
answers
68
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
Na462
asked
in
Linear Algebra
Oct 25, 2018
by
Na462
1.0k
views
linear-algebra
engineering-mathematics
system-of-equations
1
vote
1
answer
69
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??
eyeamgj
asked
in
Linear Algebra
Oct 3, 2018
by
eyeamgj
516
views
system-of-equations
2
votes
1
answer
70
Linear Algebra RGPV 2001
Test the consistency of the following system of equations and solve if possible $3x + 3y +2z = 1$ $x + 2y = 4$ $10y + 3z = -2$ $2x - 3y -z = 5$
Mk Utkarsh
asked
in
Linear Algebra
Sep 29, 2018
by
Mk Utkarsh
738
views
linear-algebra
engineering-mathematics
system-of-equations
2
votes
1
answer
71
Hk Dass Linear Algebra
Test the consistency of the following system of equations $5x + 3y + 7z = 4 $ $3x + 26y + 2z = 9$ $7x + 2y + 10z = 5$
Mk Utkarsh
asked
in
Linear Algebra
Sep 29, 2018
by
Mk Utkarsh
1.3k
views
linear-algebra
system-of-equations
1
vote
1
answer
72
Linear system of equations
Na462
asked
in
Linear Algebra
Sep 16, 2018
by
Na462
1.0k
views
engineering-mathematics
linear-algebra
system-of-equations
0
votes
1
answer
73
ISI2016-MMA-4
The $a, b, c$ and $d$ ... $(a+d)(b+c)$ equals $-4$ $0$ $16$ $-16$
go_editor
asked
in
Linear Algebra
Sep 13, 2018
by
go_editor
418
views
isi2016-mmamma
linear-algebra
matrix
system-of-equations
1
vote
1
answer
74
ISI2017-MMA-18
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
Tesla!
asked
in
Linear Algebra
Apr 25, 2018
by
Tesla!
1.5k
views
isi2017-mma
engineering-mathematics
linear-algebra
system-of-equations
3
votes
4
answers
75
ISI-2016-04
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 $-4$ $0$ $16$ $-16$
jjayantamahata
asked
in
Linear Algebra
Mar 30, 2018
by
jjayantamahata
1.5k
views
isi2016
engineering-mathematics
system-of-equations
2
votes
1
answer
76
GATE Linear Algebra
For what values of $\lambda$ the system of equations will have $2$ linear independent solutions - $x + y + z = 0$ $(\lambda + 1) y + (\lambda + 1) z = 0$ ($\lambda^{2}- 1) z = 0$ ... 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.
pilluverma123
asked
in
Linear Algebra
Mar 2, 2018
by
pilluverma123
1.2k
views
numerical-answers
linear
algebra
system
of
system-of-equations
3
votes
2
answers
77
GATE2018 ME-1: GA-7
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
Arjun
asked
in
Quantitative Aptitude
Feb 17, 2018
by
Arjun
1.3k
views
gate2018-me-1
general-aptitude
quantitative-aptitude
quadratic-equations
system-of-equations
1
vote
1
answer
78
Test Series ACE
How to solve? ________________ Number of non-negative integer solutions such that x+y+z=17 where x>1,y>2,z>3 is --------
ankit_thawal
asked
in
Linear Algebra
Jan 13, 2018
by
ankit_thawal
539
views
system-of-equations
2
votes
1
answer
79
MadeEasy Test Series: General Aptitude - System Of Equations
how to solve such questions?
charul
asked
in
Quantitative Aptitude
Jan 5, 2018
by
charul
576
views
made-easy-test-series
general-aptitude
system-of-equations
0
votes
3
answers
80
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 non-trivial 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?
stanchion
asked
in
Linear Algebra
Dec 1, 2017
by
stanchion
726
views
system
of
system-of-equations
non-trivial-solution
homogeneous-equation
1
vote
3
answers
81
NUMBER of soutions the equations have?
Consider the following system system of equations x1-2x3=0 x1-x2=0 2x1-2x2=0 No solution Infinite number of solutions Three solution unique solution
Parshu gate
asked
in
Linear Algebra
Nov 10, 2017
by
Parshu gate
469
views
engineering-mathematics
system-of-equations
1
vote
1
answer
82
Question on Solving System of Homogenous Linear Equation
While Solving System of Homogenous Linear Equations, why can't r > n i.e. rank of matrix > number of variables/unknown thanks!
iarnav
asked
in
Linear Algebra
Jun 26, 2017
by
iarnav
633
views
engineering-mathematics
linear-algebra
system-of-equations
1
vote
3
answers
83
ISRO2012-ECE: Engineering Mathematics
The system of equations $x + y + z = 6, 2x + y + z = 7, x + 2 y + z = 8$ has A unique solution No solution An infinite number of solutions None of these
sh!va
asked
in
Linear Algebra
Feb 28, 2017
by
sh!va
420
views
isro2012-ece
isro-ece
linear-algebra
system-of-equations
67
votes
9
answers
84
GATE CSE 2017 Set 1 | Question: 3
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 $Ax = b$ ... 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
Arjun
asked
in
Linear Algebra
Feb 14, 2017
by
Arjun
20.2k
views
gatecse-2017-set1
linear-algebra
system-of-equations
normal
2
votes
2
answers
85
GATE Overflow | Mathematics | Test 1 | Question: 4
Let $Ax = b$ be a system of linear equations where $A$ is a $m \times n$ matrix and $b$ is a $m \times 1$ column vector and $X$ is a $n \times 1$ column vector of unknows. Which of the following is false? The system has a ... unique solution. The system will have only a trivial solution when $m = n,$ $b$ is the zero vector and $rank (A) = n$.
Bikram
asked
in
Linear Algebra
Aug 8, 2016
by
Bikram
457
views
go-mathematics-1
linear-algebra
system-of-equations
4
votes
2
answers
86
GATE2011 GG: GA-6
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 $1$ $2$
Akash Kanase
asked
in
Quantitative Aptitude
Feb 15, 2016
by
Akash Kanase
1.3k
views
gate2011-gg
quantitative-aptitude
system-of-equations
54
votes
7
answers
87
GATE CSE 2016 Set 2 | Question: 04
Consider the systems, 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. ... $\text{II}$ and $\text{III}$ are true. Only $\text{III}$ is true. None of them is true.
Akash Kanase
asked
in
Linear Algebra
Feb 12, 2016
by
Akash Kanase
15.7k
views
gatecse-2016-set2
linear-algebra
system-of-equations
normal
2
votes
1
answer
88
TIFR-2011-Maths-A-13
$A$ is $3 \times 4$-matrix of rank $3$. Then the system of equations, $Ax = b$ has exactly one solution.
makhdoom ghaya
asked
in
Linear Algebra
Dec 9, 2015
by
makhdoom ghaya
601
views
tifrmaths2011
linear-algebra
system-of-equations
7
votes
1
answer
89
TIFR2010-Maths-B-14
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
makhdoom ghaya
asked
in
Linear Algebra
Oct 15, 2015
by
makhdoom ghaya
815
views
tifrmaths2010
linear-algebra
system-of-equations
33
votes
5
answers
90
GATE CSE 2015 Set 3 | Question: 33
If the following system has non-trivial solution, $px + qy + rz = 0$ $qx + ry + pz = 0$ $rx + py + qz = 0$, then which one of the following options is TRUE? $p - q + r = 0 \text{ or } p = q = -r$ $p + q - r = 0 \text{ or } p = -q = r$ $p + q + r = 0 \text{ or } p = q = r$ $p - q + r = 0 \text{ or } p = -q = -r$
go_editor
asked
in
Linear Algebra
Feb 15, 2015
by
go_editor
10.8k
views
gatecse-2015-set3
linear-algebra
system-of-equations
normal
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