Exercises on linear systems

1. Solve the system: .
2. Solve the system: , where t is a real number.
3. Reduce the matrix to reduced row-echelon form: .
4. Solve the homogeneous system: .
5. For which values of t the following homogeneous system has a non trivial solution? .
6. Find a condition on the real numbers a, b, c, d under which the following matrix is row-equivalent to the matrix .
7. Solve the system , where t and s are real numbers.
8. Solve the system , where t is a real number.