SOLUTION: Im really stuck! Show that the set 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 o

Question 22329: Im really stuck! Show that the set 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?
Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
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

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