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:

    eqnarray11


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

  2. Find the determinant of

    displaymath139


    Answer: The determinant is -28.

  3. Find the inverse of the matrix

    displaymath140


    Answer: The inverse is

    displaymath141

  4. Find the area of the triangle formed by the vertices tex2html_wrap_inline155 , tex2html_wrap_inline157 and (8,11).


    Answer: The area is 7.5.

  5. If tex2html_wrap_inline161 , and tex2html_wrap_inline163 find the following:

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

    eqnarray58

    Answer: The solutions are: tex2html_wrap_inline177 .

  7. If tex2html_wrap_inline179 , find the following:
  8. When is

    displaymath142


    Answer: Both expressions are equal, when the domain is restricted to the interval tex2html_wrap_inline197 .

  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.


    Answer: One such polynomial is

    displaymath143

  10. Find tex2html_wrap_inline199 , if tex2html_wrap_inline201 for tex2html_wrap_inline203 .


    Answer: tex2html_wrap_inline205 .

  11. Given the following constraints:

    eqnarray86


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Thu Jul 3 17:17:24 MDT 1997

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