LINEAR ALGEBRA (Math 211)
HW #13 (Due Wed. Nov. 15 )

1. Find the dimension of the linear space of all matrices with m rows and n columns.

In problems 2,3,4 find a basis and the dimension of a linear space spanned by the following vectors:

2. , , .

3. , , ,

4. , , ,

Find the ranks of following matrices:

5.                      6.                      7.

Find the general solutions of the following systems:

8.                      9.

10. Find the dimension and a basis of the intersection , where