Thread: simple gauss elimination prob.

For some reason I can't see how:
x+3y-z = 1
-4y + 5z = 4
can become:
x = 2-11t
y =-1+5t
z=4t

Can someone explain the step/steps between?

Originally Posted by prime_66

For some reason I can't see how:
x+3y-z = 1
-4y + 5z = 4
can become:
x = 2-11t
y =-1+5t
z=4t

Can someone explain the step/steps between?

is an under-determined system, so there will be
a free parameter in any solution. So we choose
so that it maximises the convenience of solving
the system in terms of it.

The constant on the RHS of the second equation is , as is the
coefficient of on the LHS. So setting allows
us to divide through by , and solve for in terms of .

Having found and in terms of
we just substitute these into the first equation to solve for
in terms of .

RonL

thanx, I thought z had to be equal to just t. but now i understand