Consistency of Linear System of Equations
Trending Questions
Q.
If x = cy + bz, y = az + cx, z = bx + ay where x, y, z are not all zeros, then the value of a2+b2+c2+2abc is
0
1
None of these
-1
Q. Consider the system of equations
kx+(c−1)y+z=2
cx+(k+1)y+kz=4
x+cy+z=1
Then correct statement is/are
kx+(c−1)y+z=2
cx+(k+1)y+kz=4
x+cy+z=1
Then correct statement is/are
- If c=1, then the system will be inconsistent.
- If c=1, then the may have infinite solutions.
- If k=2cosπ5 then the system will be inconsistent.
- The system can never possess infinite solutions.
Q. If the system of linear equations
2x+2y+3z=a
3x−y+5z=b
x−3y+2z=c
where a, b, c are non-zero real numbers, has more than one solution, then:
2x+2y+3z=a
3x−y+5z=b
x−3y+2z=c
where a, b, c are non-zero real numbers, has more than one solution, then:
- b+c−a=0
- b−c+a=0
- b−c−a=0
- a+b+c=0
Q. If the system of linear equations
x+ay+z=3
x+2y+2z=6
x+5y+3z=b
has no solution, then:
x+ay+z=3
x+2y+2z=6
x+5y+3z=b
has no solution, then:
- a=−1, b=9
- a=−1, b≠9
- a≠−1, b=9
- a=1, b≠9
Q. The number of values of θ∈(0, π) for which the system of linear equations x+3y+7z=0
−x+4y+7z=0
(sin3θ)x+(cos2θ)y+2z=0 has a non-trivial solution, is :
−x+4y+7z=0
(sin3θ)x+(cos2θ)y+2z=0 has a non-trivial solution, is :
- four
- three
- two
- one
Q. Let a, λ, μ∈R. Consider the system of linear equations
ax+2y=λ3x−2y=μ
Which of the following statement(s) is(are) correct?
ax+2y=λ3x−2y=μ
Which of the following statement(s) is(are) correct?
- If a=−3, then the system has infinitely many solutions for all values of λ and μ
- If a≠−3, then the system has a unique solution for all values of λ and μ
- If λ+μ=0, then the system has infinitely many solutions for a=−3
- If λ+μ≠0, then the system has no solution for a=−3
Q. Let A=[abcd] and B=[pq]≠[00]. If AB=B and a+d=2, then the value of ad−bc is
Q. The number of all possible value(s) of k for which the system of equations kx+y+z=k−1, x+ky+z=k−1, x+y+kz=k−1 has no solution is
Q. If the system of equations ax+y+z=0;x+by+z=0 and x+y+cz=0 has a non-trivial solution, then the value of 11−a+11−b+11−c is
- 1
- 2
- 0
- −1
Q. For the system of linear equations :
x−2y=1, x−y+kz=−2, ky+4z=6, k∈R,
consider the following statements :
(A) The system has unique solution if k≠2, k≠−2.
(B) The system has unique solution if k=−2.
(C) The system has unique solution if k=2.
(D) The system has no-solution if k=2.
(E) The system has infinite number of solutions if k≠−2.
Which of the following statements are correct ?
x−2y=1, x−y+kz=−2, ky+4z=6, k∈R,
consider the following statements :
(A) The system has unique solution if k≠2, k≠−2.
(B) The system has unique solution if k=−2.
(C) The system has unique solution if k=2.
(D) The system has no-solution if k=2.
(E) The system has infinite number of solutions if k≠−2.
Which of the following statements are correct ?
- (B) and (E) only
- (C) and (D) only
- (A) and (D) only
- (A) and (E) only