**MA 2071 A '02 Practice Exam 1**

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

- 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.
- 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.
- 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.

- 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.

- 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.

2002-09-06