Recent questions tagged system-of-equations

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1

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?

asked May 26 in Mathematical Logic by MRINMOY_HALDER Active (1.2k points) | 30 views

0 votes

1 answer

2

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 $2$ $-2$ $3$ $-3$

asked May 11 in Numerical Ability by akash.dinkar12 Boss (40.4k points) | 51 views

0 votes

1 answer

3

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 $1$ $-1$ $3$ $-3$

asked May 7 in Linear Algebra by Sayan Bose Loyal (6.9k points) | 113 views

+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 Boss (24.6k points) | 97 views

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0 answers

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 Loyal (6.6k points) | 69 views

+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 Loyal (6k points) | 30 views

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 Boss (34.5k points) | 88 views

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 Boss (34.5k points) | 94 views

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1 answer

9

Linear system of equations

asked Sep 16, 2018 in Linear Algebra by Na462 Loyal (6.6k points) | 62 views

0 votes

0 answers

10

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

asked Apr 25, 2018 in Linear Algebra by Tesla! Boss (17.8k points) | 178 views

+3 votes

4 answers

11

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, 2018 in Linear Algebra by jjayantamahata Active (1.3k points) | 305 views

+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

0 votes

1 answer

13

GATE2018-1-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

asked Feb 17, 2018 in Numerical Ability by Arjun Veteran (406k points) | 41 views

+1 vote

1 answer

14

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, 2018 in Linear Algebra by ankit_thawal Active (1.4k points) | 109 views

+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

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 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?

asked Dec 1, 2017 in Linear Algebra by stanchion Junior (505 points) | 132 views

0 votes

3 answers

17

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 (3.1k points) | 98 views

+29 votes

4 answers

18

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 $Ax = b$ ... 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 (406k points) | 5.1k views

0 votes

2 answers

19

GATE2011 Aptitude Set 2: 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 (41k points) | 264 views

+29 votes

3 answers

20

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 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 Boss (41k points) | 3.9k views

+1 vote

1 answer

21

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 (29.3k points) | 143 views

+2 votes

1 answer

22

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 (29.3k points) | 283 views

+5 votes

1 answer

23

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 (29.3k points) | 300 views

+20 votes

4 answers

24

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 (96.1k points) | 2.6k views

+10 votes

3 answers

25

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 (16.3k points) | 1.1k views

+22 votes

3 answers

26

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 $n \times1$ ... 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 Veteran (52k points) | 2.6k views

+17 votes

5 answers

27

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 (96.1k points) | 3.1k views

+1 vote

1 answer

28

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 (52k points) | 258 views

+14 votes

2 answers

29

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 (52k points) | 1.5k views

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