Linear Algebra Find a Basis of All 3x3 Symmetric Matrices Le

Linear Algebra: Find a Basis of All 3x3 Symmetric Matrices

Let V be the set of all symmetric 3 times 3 matrices. (Recall that V is a subspace of M_33.) Find a basis of V, and show that it is a basis.

Solution

Well,
a) dimension = 6
basis :
B11 = ( (1,0,0), (0,0,0) , (0,0,0) )
B22 = ( (0,0,0), (0,1,0) , (0,0,0) )
B33 = ( (0,0,0), (0,0,0) , (0,0,1) )
B21-12 = ( (0,1,0), (1,0,0) , (0,0,0) )
B31-13 = ( (0,0,1), (0,0,0), (1,0,0) )
B32-23 = ( (0,0,0), (0,0,1), (0,1,0) )