Recent content by moonbeam

This is what I eventually came up with and I got confirmation from a member of another math forum. Let A = span\{\left[\begin{array}{c}1\\0\\0\end{array}\right] \left[\begin{array}{c}0\\0\\1\end{array}\right]\}. Let B = span\{\left[\begin{array}{c}0\\1\\0\end{array}\right]...

The point (1, 1, 1) is not the same as the vector <1, 1, 1>. If the planes only meet at one particular point, then their intersection is just the zero vector. So the intersection of these 3 planes is still just the zero vector. I need the 3 planes to intersect in a line segment, not just one...

In this situation the subspaces A, B, and C do not satisfy the first requirement: A \cap B \cap C \neq \{\vec{0}\}. The only vector in common among the 3 planes is the zero vector. But the problem is asking for subspaces A, B, and C, that intersect in more than just the case of the zero vector.

I can't find the bases without knowing how many dimensions each subspace is. How do I even know what dimension to make the subspaces A, B, and C?

Homework Statement Find subspaces A, B, and C of \mathbb{R}^3 so that A \cap B \cap C \ne \{\vec{0}\} and (A + B) \cap C \ne A \cap C + B \cap C. You can specify a subspace by the form A = span\{\vec{e}_1, \vec{e}_2\}.Homework Equations A + B is the set of all vectors in \mathbb{R}^3 of the...

Ok, subspaces of \mathbb{R}^3 have the following properties: contain the zero vector, are closed under addition, and are closed under multiplication. Am I right? So, say A, B, and C are subspaces of \mathbb{R}^3. Then, what would (A+B) \cap C mean?

I just wanted to know if subspace A + subspace B is the same as the "union of A and B".