COURSE
MATH 3191-004: Applied Linear Algebra.
Fall 1994. University of Colorado at Denver

INSTRUCTOR
Dr. Andrew Knyazev
Office: CU (Dravo) 620G. Phone: 556-8102.
Office hours: Tue 3pm - 6pm

EXAM #5 (Chapters 1-3, 5, 6) 35% of the FINAL GRADE
Monday, December 12, 1994

  1. Let tex2html_wrap_inline30 and tex2html_wrap_inline32 be the first two components of the row-vectors u and v. Which of the following is correct for the function

    tex2html_wrap_inline34

    [A] It is an inner product for u and v in tex2html_wrap_inline40

    Correct answer [B] It is not an inner product for u and v in tex2html_wrap_inline40

    [C] It is an inner product for u and v in tex2html_wrap_inline52

    [D] The correct answer is not given by [A], [B], or [C].

  2. Which of the following is the reduced row-echelon form of the matrix
    2 0 0 0
    1 1 0 0

    [A]

    1 1 1 1
    0 1 0 0

    [B]

    1 0 0 1
    0 1 0 0

    Correct answer [C]

    1 0 0 0
    0 1 0 0

    [D] The correct answer is not given by [A], [B], or [C].

  3. Let A be the matrix

    2 0 0 0
    1 1 0 0

    Then tex2html_wrap_inline54

    [A] 2
    [B] 4
    Correct answer [C] 6

    [D] The correct answer is not given by [A], [B], or [C].

    Let A be the matrix

    2 0 0 2
    1 1 0 1
    1 2 1 1
    2 0 0 1

    for problems 4-6.

  4. det(A) =

    [A] 0
    [B] 1
    Correct answer [C] -2
    [D] -1

  5. Which of the following is an eigenvector of A?

    [A] tex2html_wrap_inline72
    [B] tex2html_wrap_inline74
    Correct answer [C] tex2html_wrap_inline76

    [D] The correct answer is not given by [A], [B], or [C]

  6. rank(A) - 3 nullity(A) =

    Correct answer [A] 4
    [B] -1
    [C] 1
    [D] 8

  7. Find the distance between the given parallel planes -4x+y-3z=1 and 8x-2y+6z=0

    [A] 1 [B] 2 [C] They are not parallel, so the distance cannot be found

    Correct answer [D] The correct answer is not given by [A], [B], or [C].

  8. Let u and v be two orthogonal unit vectors. Then tex2html_wrap_inline100

    [A] 7
    Correct answer [B] 5

    [C] It cannot be found without an additional information.

    [D] The correct answer is not given by [A],[B], or [C]

  9. Let tex2html_wrap_inline106 and tex2html_wrap_inline108 Using the Gram-Schmidt method find the orthogonal basis tex2html_wrap_inline32 of the tex2html_wrap_inline112 Then tex2html_wrap_inline114

    [A] tex2html_wrap_inline116

    [B] tex2html_wrap_inline118

    [C] tex2html_wrap_inline120

    Correct answer [D] The correct answer is not given by [A], [B], or [C].

  10. Find one of the least squares solutions of the following system

    tex2html_wrap_inline122

    tex2html_wrap_inline124

    [A] tex2html_wrap_inline126
    Correct answer [B] tex2html_wrap_inline128
    [C] tex2html_wrap_inline130

    [D] The correct answer is not given by [A],[B], or [C]


    Andrew Knyazev
    Sun Oct 26 19:00:34 MST 1997