Linear System of Equations
Trending Questions
Q.
If the system of equations and has infinitely many solutions, then ______.
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. The system of equations,
ax−y−z=α−1, x−ay−z=α−1x−y−az=α−1
has no solution if α is
ax−y−z=α−1, x−ay−z=α−1x−y−az=α−1
has no solution if α is
- Either −2 or 1
- −2
- 1
- Not −2
Q. Let each of the equations x2+2xy+ay2=0 & ax2+2xy+y2=0 represent two straight lines passing through the origin. If they have a common line, then the other two lines are given by
- x+3y=0, 3x+y=0
- 3x+y=0, 3x−y=0
- x−y=0, x−3y=0
- (3x−2y)=0, x+y=0
Q.
Let be the set of all for which the system of linear equations
has no solution. Then the set is.
is an empty set
is a singleton
contains more than two elements
contains exactly two elements
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 :
- 0
- 12
- 2
- −1
Q. For the system of equations given by, 2x+py+6z=8, x+2y+qz=5, x+y+3z=4, which of the following is/are true:
- For p≠2, q≠3, the system has unique solution.
- For p=2, q∈R, the system has infinitely many solutions.
- For p≠2, q=3, the system has no solution.
- Can't be determined.
Q. If the system of linear equations
x+y+z=5x+2y+2z=6x+3y+λz=μ ,
(λ, μ∈R), has infinitey many solutions, then the value of λ+μ is :
x+y+z=5x+2y+2z=6x+3y+λz=μ ,
(λ, μ∈R), has infinitey many solutions, then the value of λ+μ is :
- 12
- 10
- 9
- 7
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. The value of λ for which the system of equations x+y−2z=0, 2x−3y+z=0, x−5y+4z=λ is consistent is
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. Let [a] denotes 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.
If the system of equations has a non-zero solution, then the possible values of are
Q.
Let the system of linear equations, and, has a non-trivial solution. Then which of the following is true?
Q. Solution of the system of equations x+18=2y, y=2x−9 is:
- x=19, y=14
- x=13, y=12
- x=12, y=15
- x=17, y=10
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. The number of values of k for which the system of linear equations,
(k+2)x+10y=kkx+(k+3)y=k–1
has no soution, is :
(k+2)x+10y=kkx+(k+3)y=k–1
has no soution, is :
- 1
- 2
- 3
- 4
Q.
Consider the system of equations x+y+z=6, x+2y+3z=10, x+2y+λz=μ
The system has infinite solutions if:- λ≠3
- λ=3, μ=10
- λ=3, μ≠10
- none of these
Q. If A=[ab0c], then A−1+(A−aI)(A−cI)=
- 1ac[ab0−c]
- 1ac[−ab0c]
- 1ac[c−b0a]
- 1ac[cb0a]
Q. For what values of k, the system of linear equations
x+y+z=2
2x+y−z=3
3x+2y+kz=4 has a unique solution
Q. lf the system of equations x+y+z=6, x+2y+λz=0, x+2y+3z=10 has no solution,
then λ is equal to
then λ is equal to
- 2
- 3
- 4
- 5
Q. Let S be the set of all column matrices ⎡⎢⎣b1b2b3⎤⎥⎦
such that b1, b2, b3∈R and the system of equations (in real variables)
−x+2y+5z=b12x−4y+3z=b2x−2y+2z=b3
has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for each ⎡⎢⎣b1b2b3⎤⎥⎦∈S?
such that b1, b2, b3∈R and the system of equations (in real variables)
−x+2y+5z=b12x−4y+3z=b2x−2y+2z=b3
has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for each ⎡⎢⎣b1b2b3⎤⎥⎦∈S?
- x+2y+3z=b1, 4y+5z=b2 and x+2y+6z=b3
- x+y+3z=b1, 5x+2y+6z=b2 and −2x−y−3z=b3
- −x+2y−5z=b1, 2x−4y+10z=b2 and x−2y+5z=b3
- x+2y+5z=b1, 2x+3z=b2 and x+4y−5z=b3
Q. Find the value of k for which each of the following systems of equations have infinitely many solution:
4x+5y=3
kx+15y=9
4x+5y=3
kx+15y=9
Q. The system of equation λx+y+z=0, −x+λy+z=0, −x−y+λz=0 will have a non-zero solution if real values of λ are given by ................
Q. If the system of equations
x−2y+3z=9
2x+y+z=b
x−7y+az=24, has infinitely many solutions, then a−b is equal to
x−2y+3z=9
2x+y+z=b
x−7y+az=24, has infinitely many solutions, then a−b is equal to
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.
- Statement 1 is false and Statement 2 is true.
- Both the statements are true and Statement 2 is the correct explanation of Statement 1.
- Statement 1 is true and Statement 2 is false.
- Both the statements are true but Statement 2 is not the correct explanation of Statement 1.
Q. Match the equations in List 1 with the solutions in List 2
List I | List II | ||
A. | log0.25(x2+2x−8)2 −log0.5(10+3x−x2)=1 | 1. | {−3} |
B. | log2(x2+7) =5+log2x −6log2(x+7x) | 2. | {14} |
C. | log(1−2x)(6x2−5x+1)−log(1−3x)(4x2−4x+1)=2 | 3. | {16(√313−1), 12(√73−7)} |
D. | log10(1+x2−2x)+1−log10(1+x2)= 2log10(1−x) | 4. | {1, 7} |
- A- 3, B- 2, C- 1, D-4
- A- 3, B- 4, C- 1, D-2
- A- 3, B- 4, C- 2, D-1
- A- 3, B- 1, C- 2, D-4
Q. If the system of equations ax+hy+g=0, hx+by+f=0 and gx+fy+c=k
is consistent and
k=1λ∣∣ ∣∣ahghbfgfc∣∣ ∣∣, then λ is equal to
is consistent and
k=1λ∣∣ ∣∣ahghbfgfc∣∣ ∣∣, then λ is equal to
- h2−ab
- ab−h2
- h2+ab
- g2−ac
Q. The values of k∈R for which the system of equations
x+ky+3z=0,
kx+2y+2z=0
2x+3y+4z=0
admits a non-trivial solution is
x+ky+3z=0,
kx+2y+2z=0
2x+3y+4z=0
admits a non-trivial solution is
- 2
- 52
- 3
- 54
Q. If t is a real number and k=t2−t+1t2+t+1, then the system of equations
3x−y+4z=3
x+2y−3z=−2
6x+5y+kz=−3
For any allowable value of k, has
3x−y+4z=3
x+2y−3z=−2
6x+5y+kz=−3
For any allowable value of k, has