(adsbygoogle = window.adsbygoogle || []).push({}); Vector Subspaces, don't understand....

1. The problem statement, all variables and given/known data

Which of the given subsets of the vector space, M_{23}, of all 2 X 3 matrices are subspaces.

(a) [a b c, d 0 0] where b = a + c

2. Relevant equations

Theorem 4.3

Let V be a vector space with operations + and * and let W be a nonempty subset of V. Then W is a subspace of V if and only if the following conditions hold

(a) u and v are any vectors in W, thenu+ v is in W.

(b) If c is any real number and u is any vector in W, then c * u is in W.

3. The attempt at a solution

First of all I'm not exactly sure what the space R^{3}exactly is and what to look for.

Is it all the positive numbers in x,y and z? I know what two properties to apply when trying to figure out if its a subspace but I still don't know exactly what to look for.

If someone could explain how to look at this problem, anything about vector spaces, or point me in the direction of a good website about them that would be greatly appreciated...i have yet to find one that I like. Thanks!!

**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: Vector Subspaces, don't understand

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