I am unable to get the answer to the following question: Find all the values of (x,y,z) which satisfy:
if (p,q,r) satisfies
So, we have:
detA = 7(-1) -2(-2) + 4(1) = 1. So it has an inverse. I used two methods to calculate the inverse, the adjoint and row reduction. Both gave the same result:
The second matrix B is singular i.e.
But we have the following relationships:
I messed around and got:
p = 7x + 2y + 4z
q = 4x + y + 2z
r = 3x + y + z
but this doesn't help. The answers are given in terms of Am I missing something here?
I took the matrix:
Then using row reduction, I converted it into an equivalent triangular matrix:
which gives a consistent result:
x + 2y - z = 5 (i)
-4y + 8z = -8 (ii)
0z = 0 (iii)
The last equation is true for any z, so I can set and everything is fine.
Previously I made an arithmetic error so that the equations appeared inconsistent with no solutions. I checked the result once and then twice and then posted. I think the best advice when doing matrix questions is not to post after a late night. Try again in the morning and things are usually a lot clearer! Anyway, thanks again guys.