LINEAR ALGEBRA (Math 211)
HW #12 (Due Wed. Nov. 8 )

1. Find the dimension of the linear space of all 2 x 2 matrices and give an example of a basis in it.

2. Prove that the vectors , , and form a basis in and compute the coordinates of vector with respect to this basis.

3. For vectors , , and find the dimension . Which of the vectors , , form a basis of this space?

4. Find the rank of matrix .

5. Find a basis of the kernel of matrix .

6. Let be the zero vector. Prove that the vectors , , , ..., are always linearly dependent for any vectors , , ..., .