MA-305 Homework 5

Due at 2:35 pm, Tuesday, April 7, 1998


Calculations necessary for these problems may be done either by hand or with Maple. Solutions may be submitted in person in class, or you may email an ASCII text, Maple Text, or Maple Worksheet (.mws) to the TA, John Haws (jchaws@eos.ncsu.edu).

Remember: If you have a question, you may find the answer in the Forum.

  1. Let W=span{(1,1,1),(1,2,-2)}.
    1. Find a basis for the orthogonal complement of W.
    2. Describe the orthogonal complement of W geometrical.

  2. For the given matrix, find (i) a basis for its row space, (ii) a basis for its column space, and (iii) its rank.
    1. [
      [
      [
      [       		6
      12
      -3
      9       		4
      8
      -2
      6       		-8
      -14
      6
      -11       		2
      6
      1
      4       		10
      2
      2
      6       		]
      ]
      ]
      ]
    2. [
      [
      [       		1
      1
      -1       		1
      2
      2       		2
      3
      1       		]
      ]
      ]

  3. Let u=(1,1,4) and v=(-2,5,1).
    Compute
    1. u·v, the scalar product of u and v.
    2. ||u - v||, the Euclidean norm of u - v.
    3. the angle between u and v.
    4. the projection of u onto v.