Linear System of Equations
Trending Questions
Q. The following system of linear equations
7x+6y−2z=0,
3x+4y+2z=0
x−2y−6z=0, has
7x+6y−2z=0,
3x+4y+2z=0
x−2y−6z=0, has
- infinitely many solutions, (x, y, z) satisfying y=2z
- infinitely many solutions (x, y, z) satisfying x=2z
- no solution
- only the trivial solution
Q. Let [a] denote the integral part of a and x=a3y+a2z, y=a1z+a3x and z=a2x+a1y, where x, y, z are not all zero. If a1=m−[m], m being a non-integral constant, then the least integral value of |a1a2a3| is
Q. The system of equations
−2x+y+z=a, x−2y+z=b, x+y−2z=c has:
−2x+y+z=a, x−2y+z=b, x+y−2z=c has:
- no solution if a+b+c≠0
- unique solution if a+b+c=0
- infinte number of solutions if a+b+c=0
- infinte solution if a+b+c≠0
Q. If the system of equations ax+y=3, x+2y=3 and 3x+4y=7 is consistent, then value of a is
- 0
- 1
- 2
- −1
Q. Given a, b∈{0, 1, 2, 3, 4.....20}. Consider the system of equations
x + y + 2z =5
2x + y + 3z = 6
x + 2y + az =b
Let
'A' denotes number of ordered pairs (a, b) so that the system of equations has unique solution.
'B' denotes number of ordered pairs (a, b) so that the system of equations has no solution.
'C' denotes number of ordered pairs (a, b) so that the sytem of equations has infinite solutions.
then which of the following is/are correct?
x + y + 2z =5
2x + y + 3z = 6
x + 2y + az =b
Let
'A' denotes number of ordered pairs (a, b) so that the system of equations has unique solution.
'B' denotes number of ordered pairs (a, b) so that the system of equations has no solution.
'C' denotes number of ordered pairs (a, b) so that the sytem of equations has infinite solutions.
then which of the following is/are correct?
- A = 400
- B = 20
- C = 21
- A+ B = 440
Q. The value(s) of k∈R for which the system of equations
x+ky+3z=0,
kx+2y+2z=0 and
2x+3y+4z=0
admits a non-trivial solution, is
x+ky+3z=0,
kx+2y+2z=0 and
2x+3y+4z=0
admits a non-trivial solution, is
- 2
- 52
- 3
- 54
Q. Let a, b and c be positive real numbers. The following system of equations in x, y and z
x2a2+y2b2−z2c2=1, x2a2−y2b2+z2c2=1, −x2a2+y2b2+z2c2=1 has
x2a2+y2b2−z2c2=1, x2a2−y2b2+z2c2=1, −x2a2+y2b2+z2c2=1 has
- no solution
- unique solution
- infinitely many solutions
- finitely many solutions
Q. If the system of linear equations
x−2y+kz=12x+y+z=23x−y−kz=3
has a solution (x, y, z), z≠0, then (x, y) lies on the straight line whose equation is :
x−2y+kz=12x+y+z=23x−y−kz=3
has a solution (x, y, z), z≠0, then (x, y) lies on the straight line whose equation is :
- 4x−3y−1=0
- 3x−4y−1=0
- 3x−4y−4=0
- 4x−3y−4=0
Q. The system of equations
kx+(k+1)y+(k−1)z=0
(k+1)x+ky+(k+2)z=0
(k−1)x+(k+2)y+kz=0 has a non-trivial solution for
kx+(k+1)y+(k−1)z=0
(k+1)x+ky+(k+2)z=0
(k−1)x+(k+2)y+kz=0 has a non-trivial solution for
- Exactly three values of k
- Exactly two real values of k
- Exactly one real value of k
- Infinite real values of k
Q. An ordered pair (α, β) for which the system of linear equations
(1+α)x+βy+z=2αx+(1+β)y+z=3αx+βy+2z=2
has a unique solution, is:
(1+α)x+βy+z=2αx+(1+β)y+z=3αx+βy+2z=2
has a unique solution, is:
- (1, −3)
- (−3, 1)
- (−4, 2)
- (2, 4)
Q. Consider the system of equations
x+y+z=6,
x+2y+3z=10 and
x+2y+λz=μ
Statement 1: If the system has infinite number of solutions, then μ=10.
Statement 2: The value of ∣∣ ∣∣116121012μ∣∣ ∣∣=0 for μ=10.
x+y+z=6,
x+2y+3z=10 and
x+2y+λz=μ
Statement 1: If the system has infinite number of solutions, then μ=10.
Statement 2: The value of ∣∣ ∣∣116121012μ∣∣ ∣∣=0 for μ=10.
- Both the statements are true and Statement 2 is the correct explanation of Statement 1.
- Both the statements are true but Statement 2 is not the correct explanation of Statement 1.
- Statement 1 is true and Statement 2 is false.
- Statement 1 is false and Statement 2 is true.
Q. If S is the set of distinct values of ‘b′ for which the following system of linear equations
x+y+z=1x+ay+z=1ax+by+z=0
has no solution, then S is:
x+y+z=1x+ay+z=1ax+by+z=0
has no solution, then S is:
- an empty set
- an infinite set
- a finite set containing two or more elements
- a singleton
Q. The greatest value of c∈R for which the system of linear equations
x−cy−cz=0cx−y+cz=0cx+cy−z=0
has a non-trivial solution, is :
x−cy−cz=0cx−y+cz=0cx+cy−z=0
has a non-trivial solution, is :
- −1
- 0
- 12
- 2
Q. Let [a] denote the integral part of a and x=a3y+a2z, y=a1z+a3x and z=a2x+a1y, where x, y, z are not all zero. If a1=m−[m], m being a non-integral constant, then the least integral value of |a1a2a3| is
Q. Given a, b∈{0, 1, 2, 3, 4.....20}. Consider the system of equations
x + y + 2z =5
2x + y + 3z = 6
x + 2y + az =b
Let
'A' denotes number of ordered pairs (a, b) so that the system of equations has unique solution.
'B' denotes number of ordered pairs (a, b) so that the system of equations has no solution.
'C' denotes number of ordered pairs (a, b) so that the sytem of equations has infinite solutions.
then which of the following is/are correct?
x + y + 2z =5
2x + y + 3z = 6
x + 2y + az =b
Let
'A' denotes number of ordered pairs (a, b) so that the system of equations has unique solution.
'B' denotes number of ordered pairs (a, b) so that the system of equations has no solution.
'C' denotes number of ordered pairs (a, b) so that the sytem of equations has infinite solutions.
then which of the following is/are correct?
- A = 400
- B = 20
- C = 21
- A+ B = 440
Q. Match the following for system of linear equations
2x -3y + 5z =12
3x+y+λz=μ
x -7y + 8z =17
Column - IColumn - I(P)Unique solution(1)λ=2, μ=7(Q)Infinite solution(2)λ≠2, μ=7(R)No solution(3)λ≠2, μ≠7(S)Consistent system(4)λ∈R, μ≠7equation(5)λ=2, μ≠7
2x -3y + 5z =12
3x+y+λz=μ
x -7y + 8z =17
Column - IColumn - I(P)Unique solution(1)λ=2, μ=7(Q)Infinite solution(2)λ≠2, μ=7(R)No solution(3)λ≠2, μ≠7(S)Consistent system(4)λ∈R, μ≠7equation(5)λ=2, μ≠7
- P→2;Q→1;R→5;S→1, 2
- P→2, 3;Q→1;R→5;S→1, 2, 3
- P→2, 3;Q→1;R→4, 5;S→1, 2, 3
- P→3;Q→1;R→4, 5;S→2, 3