Precalculus Practice Exam

Part 4 Test 6 Time: 2 hours

Matrix Algebra is no longer included in Math 4109.

1. Solve the following system of equations using Matrices:

Answer: The solutions are: x=3, y=1, z=2.

2. Find the determinant of

3. Find the inverse of the matrix

4. Find the area of the triangle formed by the vertices , and (8,11).

5. If , and find the following:
• 3A-4B

• .

6. Find all the solutions of the following system of linear equations:

7. If , find the following:
• Vertex.

Answer: The vertex is (4, -11).

• Axis of Symmetry.

Answer: The axis of symmetry is x=4.

• Minimum Value.

Answer: The minimum value is y=-11.

• Maximum Value.

Answer: There is no maximum value.

• Domain of f(x).

Answer: The domain of f(x) is the set of all real numbers, or in interval notation, .

• Range of f(x).

Answer: The range of f(x) is the set of all .

8. When is

Answer: Both expressions are equal, when the domain is restricted to the interval .

9. Find a polynomial with zero of 7 of multiplicity 3, zero of -1 of multiplicity of 4, zero of 0 with multiplicity 2, and zero of 1-i, of multiplicity 3.

10. Find , if for .

11. Given the following constraints:

• Find the maximum value of z=3x-5y.

Answer: The maximum value is 18 at x=6, and y=0.

• Find the minimum value of x=3x-5y.

Answer: The minimum value is 0 at x=0, and y=0.

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Thu Jul 3 17:17:24 MDT 1997