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Recent questions tagged systemofequations
+1
vote
3
answers
1
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
(
1.5k
points)

105
views
isi2016
engineeringmathematics
systemofequations
+1
vote
0
answers
2
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
(
277
points)

63
views
numericalanswers
linear
algebra
system
of
systemofequations
+1
vote
0
answers
3
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)

71
views
systemofequations
0
votes
3
answers
4
Linear Homogeneous Equation (Allen 2017)
asked
Dec 1, 2017
in
Linear Algebra
by
stanchion
(
425
points)

89
views
system
of
systemofequations
nontrivialsolution
homogeneousequation
0
votes
3
answers
5
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
(
4.9k
points)

66
views
engineeringmathematics
systemofequations
+21
votes
3
answers
6
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
(
347k
points)

3.2k
views
gate20171
linearalgebra
systemofequations
normal
0
votes
2
answers
7
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
(
42.5k
points)

194
views
gate2011_gg
numericalability
systemofequations
+24
votes
3
answers
8
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
(
42.5k
points)

2.6k
views
gate20162
linearalgebra
systemofequations
normal
+1
vote
1
answer
9
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
(
40k
points)

108
views
tifrmaths2011
linearalgebra
systemofequations
+2
votes
1
answer
10
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
(
40k
points)

236
views
tifr2014
linearalgebra
systemofequations
+5
votes
1
answer
11
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
(
40k
points)

242
views
tifrmaths2010
linearalgebra
systemofequations
+17
votes
2
answers
12
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
(
98.5k
points)

1.8k
views
gate20153
linearalgebra
systemofequations
normal
+9
votes
3
answers
13
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
Boss
(
19.1k
points)

725
views
gate2004it
linearalgebra
systemofequations
easy
+19
votes
2
answers
14
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
(
59.4k
points)

1.5k
views
gate1996
linearalgebra
systemofequations
normal
+16
votes
4
answers
15
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
(
98.5k
points)

2k
views
gate20141
linearalgebra
systemofequations
numericalanswers
normal
+1
vote
0
answers
16
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
(
59.4k
points)

174
views
gate1998
linearalgebra
systemofequations
descriptive
+11
votes
3
answers
17
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
(
59.4k
points)

953
views
gate1998
linearalgebra
systemofequations
easy
+8
votes
2
answers
18
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
(
18k
points)

697
views
gate2005
linearalgebra
systemofequations
normal
+11
votes
3
answers
19
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
(
59.4k
points)

998
views
gate2004
linearalgebra
systemofequations
normal
+15
votes
2
answers
20
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
Veteran
(
59.4k
points)

1.8k
views
gate2003
linearalgebra
systemofequations
normal
+14
votes
2
answers
21
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
(
59.4k
points)

1.5k
views
gate2008
easy
linearalgebra
systemofequations
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