I need a little help... just can't figure this question out.
Using gaussian elimination I got (2-b)z = 2 - b.For what values of a and b does the system
ax + bz = 2
ax + by + 4z = 4
ay + 2z = b
- (i) no solution
- (ii) a unique solution
- (iii) a one parameter solution
- (iv) a two parameter solution
Substituting a=0 gives z=1 and b=2 but nothing for x or y so at a guess that would be the 1 parameter solution.
Substituting b=0 gives ax=2, ay+4z=4 and ay+2z = 0. Rearranging and subsituting gives 2z=4 so z=2, and -ay=4. So -ay=2ax which means -y=2x
That is all I could think to do.