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 , , ..., .