Spanning set of matrices?

[paulrb]

Homework Statement

Find a spanning set for the space of all 3x3 symmetric matrices.

Homework Equations

The Attempt at a Solution

I know how to find the spanning set for vectors, but I don't know if it works the same way for matrices. Is the set's elements matrices? If so, would this be it?

|100| |010| |001| |000| |000| |000|
|000| |100| |000| |010| |001| |000|
|000| |000| |100| |000| |010| |001|

Sorry if that's messy, I'm not sure what the normal way of typing matrices is.

 

[Russell Berty]

Notice that addition and scalar multiplication for vectors and matrices are defined the same way.

Notice also that the matrix | 1 4 |
| 3 7 |
(an array of numbers, a "list")
can be represented as <1 ,4, 3, 7> (a list) which is a vector.