Welcome to our community

Be a part of something great, join today!

Subspace of three equations

Johnathon

New member
May 18, 2019
2
S is the set of solutions for the set of three equations...

x + (1 - a)y-1 + 2z + b2w = 0
ax + y - 3z + (a - a2)|w| = a3 - a
x + (a - b)y + z + 2a2w = b

I worked out...

The first equation is a subset of R4 when a = 1, b is any real.

The second equation is a subset of R4 when a = 1 or a = 0.

The third equation is a subset of R4 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 R4.

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