Recent questions tagged system-of-equations

+1 vote

1 answer

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 Boss (16.1k points) | 37 views

0 votes

0 answers

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 Loyal (6.9k points) | 41 views

+1 vote

0 answers

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 Loyal (5.8k points) | 20 views

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 Boss (23.7k points) | 51 views

0 votes

1 answer

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 Boss (23.7k points) | 42 views

0 votes

1 answer

6

Linear system of equations

asked Sep 16 in Linear Algebra by Na462 Loyal (6.9k points) | 31 views

+2 votes

4 answers

7

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 $-4$ $0$ $16$ $-16$

asked Mar 31 in Linear Algebra by jjayantamahata Active (1.6k points) | 172 views

+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

+1 vote

1 answer

9

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 --------

asked Jan 13 in Linear Algebra by ankit_thawal Active (2.1k points) | 92 views

0 votes

3 answers

10

Linear Homogeneous Equation (Allen 2017)

asked Dec 1, 2017 in Linear Algebra by stanchion Junior (505 points) | 106 views

0 votes

3 answers

11

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

asked Nov 10, 2017 in Linear Algebra by Parshu gate Active (5k points) | 75 views

+23 votes

4 answers

12

GATE2017-1-3
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 $Ax = b$ 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

0 votes

2 answers

13

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 $1$ $2$

asked Feb 16, 2016 in Numerical Ability by Akash Kanase Boss (43k points) | 211 views

+26 votes

3 answers

14

GATE2016-2-04
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

+1 vote

1 answer

15

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.

asked Dec 9, 2015 in Linear Algebra by makhdoom ghaya Boss (40.4k points) | 122 views

+2 votes

1 answer

16

TIFR2014-A-1
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

+5 votes

1 answer

17

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

asked Oct 15, 2015 in Linear Algebra by makhdoom ghaya Boss (40.4k points) | 261 views

+17 votes

4 answers

18

GATE2015-3-33
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? $p - q + r = 0 \text{ or } p = q = -r$ $p + q - r = 0 \text{ or } p = -q = r$ $p + q + r = 0 \text{ or } p = q = r$ $p - q + r = 0 \text{ or } p = -q = -r$

asked Feb 15, 2015 in Linear Algebra by jothee Veteran (106k points) | 2k views

+9 votes

3 answers

19

GATE2004-IT-6
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) | 823 views

+20 votes

3 answers

20

GATE1996-1.7
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

+16 votes

5 answers

21

GATE2014-1-4
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

+1 vote

0 answers

22

GATE1998-9
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

+12 votes

3 answers

23

GATE1998-1.2
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

+8 votes

2 answers

24

GATE2005-48
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

+12 votes

4 answers

25

GATE2004-71
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

+16 votes

2 answers

26

GATE2003-41
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 (59.6k points) | 2.1k views

+15 votes

2 answers

27

GATE2008-3
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

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