||Time: 2 hours
Matrix Algebra is no longer included in Math 4109.
- 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:
- Find all the solutions of the following system of linear equations:
Answer: The solutions are:
- If , find the following:
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
- 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
Answer: One such polynomial is
- Find , if for .
- 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
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