Math 232 Homework Assignment 02

- Due 4:30 PM Monday, January 24th 2000

• Section 1.3, pages 46 - 48:
  • 14, 18, 22, 26, 36, 42

• Section 1.4, pages 68 - 71:
  • 2(b), 4(b), 6(b), 8 ,10, 12, 14, 16, 18, 20 ,26, 28
    (Use the Gauss-Jordan method for 14-20.)

• Maple Exercises:
  Staple these Maple Exercises to the end of all your handwritten work.
  • Section 1.3
    (See the posted Intro to Matrices in Maple.)
    1. Using a functional operator, make the following matrix:
       

    2. Using a functional operator, make the following matrix:
       
       [Hint: you will need an if statement in your functional operator.
       You can use Maple's type command to check if something is even or odd, as in if type(m+n,even) then...]

    3. Do Sec. 1.3 M1(a)-(c) using the above matrices for A and B.
       [Hint: you will need Maple's transpose command, as in transpose(B).]

  • Section 1.4
    (See the posted Gauss Reduction and the Gauss-Jordan Method in Maple.)
    1. Make a 4 by 5 matrix of random integers between -10 and 10.
       [Hint: use rand(-10..10) as the third argument of matrix.]

    2. Treat this as an augmented matrix for a system of 4 linear equations in 4 variables, and use the gaussjord command to convert the matrix into reduced row echelon form.

    3. Now do it the long way using elementary row operations (swaprow, mulrow, and addrow), and compare the two answers.