MA 2071 A '02 Practice Exam 1

1. Solve the linear system below, using the method of elimination.

2. Suppose is a square matrix. Use the properties of matrix operations to show that is symmetric. Make sure you note which properties you are using.

3. Suppose that is an invertible, square matrix. Use the properties of the inverse to show that the equation always has a unique solution. Make sure you note which properties you are using.

4. Solve the linear system below, using the method of Gauss-Jordan reduction. You must show all of your steps in converting the augmented matrix to reduced row echelon form.

5. Solve the homogeneous linear system below, using the method of Gauss-Jordan reduction. You must show all of your steps in converting the augmented matrix to reduced row echelon form.

6. Show that the matrix

is nonsingular, and compute its inverse. You may use either the formula given in class for a matrix, or the general method involving RREF.

William W. Farr
2002-09-06