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