1. Nov 10, 2009

### hahatyshka

hi can someone tell me...how to correctly use the 10 axioms..
for example: does the set of all 3x3 symmetric matrices form a subspace of a 3x3 matrices under the normal operations of matrix addition and multiplication?
I don't really get how to prove this..

2. Nov 10, 2009

### HallsofIvy

Staff Emeritus

The only things you need to prove are that the set is closed under addition and scalar multiplication. Suppose
$$A= \begin{bmatrix}a & b & c \\b & d & e \\c & e & f\end{bmatrix}$$
and
$$B= \begin{bmatrix} u & v & w \\ v & x & y \\w & y & z\end{bmatrix}$$
two symmetric matrices. Is A+ B symmetric? Is $\alpha A$ symmetric for any number $\alpha$?

3. Nov 13, 2009

### Legion81

I thought a subspace had to also contain the zero vector (not empty), or am I remembering that wrong?

4. Nov 14, 2009

### HallsofIvy

Staff Emeritus