Homework Statement
Find the basis of the solution space W \subset \Re^{4}
of the system of linear equations
2x_{1} + 1x_{2} + 2x_{3} +3x_{4} =0
_{ }
1x_{1} + 1x_{2} + 3x_{3} = 0
Homework Equations
The basis must span W and be independent.
The Attempt at a Solution
Solving...
What? I can only assume you're asking if I go to Washington. No, It's just the problem comes straight from a common algebra textbook and I'm in the same chapter.
Alright, I've just about got a solution now, this should get you started on the right track:
I was right previously, we are not looking for a number r such that s(n)*r = 1, but for a map. The right inverse of s would mean that s(r(n)) = n for all n in the natural numbers. Can you prove that r...
Hey, I'm working on the same problem, and equally stuck. Here's a line of thought I think might be the key.
We aren't looking for an inverse such that s*R = 1, because s isn't a number, it's a map. The definition of s*R = 1 is for an element s. What s is an element of is the maps N -> N, so...