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## Homework Statement

Exercise 1: For what value of m will the following system of linear equations have infinitely many solutions?

mx + 3y = 12

2x + (1/2)y = 5

Exercise 2: For what value of k will the following system of linear equations

x + 2y + kz = 1

2x + ky + 8z = 3

have

a) unique solution?

b) no solution?

c) more than one solution?

3. Discuss the following system:

x + z + w = 0

x + ky + k²w = 1

x + (k + 1)z + w = 1

x + z + kw = 2

**2. The attempt at a solution**

I've put this questions together because they are all related... I hope it's ok to do so.

Honestly I don't know what to do. I know how to do the Gauss' Elimination and Crammer's Rule but I don't see how to apply them. I mean, for the second one, can I just say that if k = 4 the system will have no solution because I'll get 1 = 3? Or do I have to show it by using one of those techniques?

Can you guys point me out the right direction? I mean, help me to understand what to do?

Thanks in advance.