Precalculus I--Part 4--Test 6--With Answers

Precalculus Practice Exam

Part 4 Test 6 Time: 2 hours

Solve the following system of equations using Matrices:

Answer: The solutions are: x=3, y=1, z=2.
Find the determinant of

Answer: The determinant is -28.
Find the inverse of the matrix

Answer: The inverse is
Find the area of the triangle formed by the vertices , and (8,11).

Answer: The area is 7.5.
If , and find the following:
- 3A-4B
  
  Answer:
- Answer:
- .
  
  Answer:
Find all the solutions of the following system of linear equations:

Answer: The solutions are: .
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 .
When is

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

Answer: One such polynomial is
Find , if for .

Answer: .
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.