Write a system of linear equations consisting of three equations in three unknowns with
(a) no solutions.
(b) exactly one solution.
(c) infinitely many solutions.

How do I go about doing this? Any help?

Question

Write a system of linear equations consisting of three equations in three unknowns with
(a) no solutions.
(b) exactly one solution.
(c) infinitely many solutions.

How do I go about doing this? Any help?

badhi · Answer

If one equation from the three equations can be derived from another equation or both of the other two equations it has infinitely many solutions. For example, if three equations were,

5x+7y+9z=15 and 10x+14y+18z=30, 14x+3y+5z = 35 second equation is 2 times the first equation. So ultimately you will end up with two independent equations with three variables which will give infinitely many solutions.

If two of the three equations were like this,

7x+3y+10z=30 and 7x+3y+10z=15, you will get no solution since no combination of x,y,z value will give 7x+3y+10z both 30 and 15 at the same time.

anonymous · Answer

This makes sense @BAdhi 
I'm taking linear algebra for the first time.

badhi · Answer

Good luck with that. It sure is an interesting subject :)

anonymous · Answer

I hope it is