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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 _______?

Question 4

The following system of homogeneous equations has non-trivial solution, then 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?

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 = _______.
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