Recent questions tagged system-of-equations

+1 vote

1 answer

1

ISI2014-DCG-9
The values of $\eta$ for which the following system of equations $\begin{array} {} x & + & y & + & z & = & 1 \\ x & + & 2y & + & 4z & = & \eta \\ x & + & 4y & + & 10z & = & \eta ^2 \end{array}$ has a solution are $\eta=1, -2$ $\eta=-1, -2$ $\eta=3, -3$ $\eta=1, 2$

asked Sep 23, 2019 in Linear Algebra by Arjun Veteran (430k points) | 74 views

0 votes

1 answer

2

ISI2014-DCG-64
The value of $\lambda$ such that the system of equation $\begin{array}{} 2x & – & y & + & 2z & = & 2 \\ x & – & 2y & + & z & = & -4 \\ x & + & y & + & \lambda z & = & 4 \end{array}$ has no solution is $3$ $1$ $0$ $-3$

asked Sep 23, 2019 in Linear Algebra by Arjun Veteran (430k points) | 59 views

0 votes

1 answer

3

ISI2015-MMA-43
The values of $\eta$ for which the following system of equations $\begin{array} {} x & + & y & + & z & = & 1 \\ x & + & 2y & + & 4z & = & \eta \\ x & + & 4y & + & 10z & = & \eta ^2 \end{array}$ has a solution are $\eta = 1, -2$ $\eta = -1, -2$ $\eta = 3, -3$ $\eta = 1, 2$

asked Sep 23, 2019 in Linear Algebra by Arjun Veteran (430k points) | 27 views

0 votes

1 answer

4

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

asked Sep 23, 2019 in Linear Algebra by Arjun Veteran (430k points) | 27 views

0 votes

1 answer

5

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

asked Sep 18, 2019 in Linear Algebra by gatecse Boss (17.5k points) | 25 views

0 votes

1 answer

6

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

asked Sep 18, 2019 in Linear Algebra by gatecse Boss (17.5k points) | 14 views

0 votes

0 answers

7

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, 2019 in Mathematical Logic by MRINMOY_HALDER Active (3.8k points) | 39 views

0 votes

1 answer

8

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, 2019 in Numerical Ability by akash.dinkar12 Boss (42.4k points) | 85 views

+1 vote

1 answer

9

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, 2019 in Linear Algebra by Sayan Bose Loyal (7.4k points) | 157 views

+1 vote

1 answer

10

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 (29k points) | 127 views

0 votes

0 answers

11

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 (7k points) | 87 views

+1 vote

0 answers

12

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 (6.2k points) | 34 views

0 votes

1 answer

13

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 (36.4k points) | 99 views

0 votes

1 answer

14

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 (36.4k points) | 115 views

0 votes

1 answer

15

Linear system of equations

asked Sep 16, 2018 in Linear Algebra by Na462 Loyal (7k points) | 80 views

0 votes

1 answer

16

ISI2016-MMA-4
The $a, b, c$ and $d$ ... $(a+d)(b+c)$ equals $-4$ $0$ $16$ $-16$

asked Sep 13, 2018 in Linear Algebra by jothee Veteran (105k points) | 32 views

0 votes

0 answers

17

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 (18.4k points) | 197 views

+3 votes

4 answers

18

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 (1.5k points) | 428 views

+1 vote

1 answer

19

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) | 174 views

0 votes

1 answer

20

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

asked Feb 17, 2018 in Numerical Ability by Arjun Veteran (430k points) | 96 views

+1 vote

1 answer

21

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) | 117 views

+2 votes

1 answer

22

MadeEasy Test Series: General Aptitude - System Of Equations
how to solve such questions?

asked Jan 5, 2018 in Numerical Ability by charul Junior (823 points) | 197 views

0 votes

3 answers

23

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 (555 points) | 141 views

0 votes

3 answers

24

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) | 111 views

+34 votes

5 answers

25

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 (430k points) | 6.3k views

0 votes

2 answers

26

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 (41.9k points) | 307 views

+32 votes

3 answers

27

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 (41.9k points) | 4.5k views

+1 vote

1 answer

28

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 (30.7k points) | 159 views

+5 votes

1 answer

29

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 (30.7k points) | 318 views

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