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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!!

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# Vector Subspaces, don't understand

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