I have 2 subspaces U and V of R^3 which(adsbygoogle = window.adsbygoogle || []).push({});

U = {(a1, a2, a3) in R^3: a1 = 3(a2) and a3 = -a2}

V = {(a1, a2, a3) in R^3: a1 - 4(a2) - a3 = 0}

I used the information in U and substituted it into the equation in V and I got 0 = 0. So, does it mean that the intersection of U and V is the whole R^3 which has no restrictions on a1, a2 and a3 (they are free)? Or do the original restrictions on both the original subspaces still being applied to the intersection?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Intersection of subspaces

**Physics Forums | Science Articles, Homework Help, Discussion**