Question 22329
 S= 2X2 matrx (a 0 (1st row) and 0 b (2nd row)) is a subspace of the vector space of ALL 2X2 matrices. Give basis for S. What is the dimension of S? 
 (a 0)
 (0 b)

 Note that the set all 2x2  matrices (say over R) is 
 a v.s. of dim 2x2 = 4.(why ?)

 Now, S contains two indep. matrices
 (1 0)
 (0 0) and

 (0 0)
 (0 1)
 they form a basis of S and dim S = 2 (why ?)

 Kenny