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- #1

x + (1 - a)y

^{-1}+ 2z + b

^{2}w = 0

ax + y - 3z + (a - a

^{2})|w| = a

^{3}- a

x + (a - b)y + z + 2a

^{2}w = b

I worked out...

The first equation is a subset of R

^{4}when a = 1, b is any real.

The second equation is a subset of R

^{4}when a = 1 or a = 0.

The third equation is a subset of R

^{4}when b = 0 and a is any real.

Now, I'm trying to work out the values of a and b that make S a subspace of R

^{4}.

Isn't S only a subspace for the values of a and b that are common to all three equations?