Applied Linear Algebra

Quiz 1

Due 2 March 1999

This is a take-home group quiz. A group should consist of 3-4 students. One solution set per group is accepted.

Cite all major theorems and show all relevant work. Please do each question on a separate page.

  1. Let V be the vector space over the field of real numbers tex2html_wrap_inline21 of all complex-valued polynomials of one complex variable x having degree at most 4. Determine the dimension and find a basis of V.
  2. Let V be the real vector space from the previous problem, and

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    be its subspace. Let V/L be the factor space.
    Let tex2html_wrap_inline33 be the class of elements comparable with an element

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    tex2html_wrap_inline37 be the class of elements comparable with an element

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    and tex2html_wrap_inline41 be the class of elements comparable with an element

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    where tex2html_wrap_inline45 . Is the following true: X + Y = Z ?

  3. Determine using the Laplace theorem the set of all real numbers tex2html_wrap_inline49 for which tex2html_wrap_inline51 , where A is the matrix

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  4. Compute the determinant of the following n-by-n matrix:

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Andrew Knyazev
Thu Feb 18 19:11:00 MST 1999