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Non-Homogeneous System Starter Quiz-4
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Question 1
Consider the system of linear equations:
x + y + z = 8
2x + 3y + 5z = 8
4x + 5z = 2
The given system of equations has __________.
Question 2
Suppose a system of linear equations which consists of m equations. If the number of variables in a particular equation is n, then which of the following is true regarding the above specification?
Question 3
The system of linear equations
x+y+z=2, 2x+y-z=3, 3x+2y+kz=4
has unique solution if _______?
x+y+z=2, 2x+y-z=3, 3x+2y+kz=4
has unique solution if _______?
Question 4
The following system of homogeneous equations:
2x + y + 2z = 0
x + y + 3z = 0
4x + 3y + bz = 0
has non-trivial solution, then the value of b is ___________?
2x + y + 2z = 0
x + y + 3z = 0
4x + 3y + bz = 0
has non-trivial solution, then the value of b is ___________?
Question 5
Consider the following system of equations.
x+y = 2
x+py = 2
where p is constant. Find the value of ‘p’ such that the system has more than two solutions?
x+y = 2
x+py = 2
where p is constant. Find the value of ‘p’ such that the system has more than two solutions?
Question 6
If the system of equations
x – ky – z = 0, kx – y – z = 0, x + y – z = 0 has a non-zero solution, then the possible values of k are: ‘–a’ and ‘b’ then ⎪a + b⎪ = _______.
x – ky – z = 0, kx – y – z = 0, x + y – z = 0 has a non-zero solution, then the possible values of k are: ‘–a’ and ‘b’ then ⎪a + b⎪ = _______.
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