MECH102 - Homework Hints, Answers, and Extra Requirements

Homework 5 (from Chapter 9)

TO ENHANCE YOUR LEARNING, PLEASE TRY TO WORK THE PROBLEMS FIRST WITHOUT LOOKING AT THE HINTS AND ANSWERS BELOW.

MAKE SURE YOU SATISFY ALL REQUIREMENTS LISTED BELOW AND IN THE ORIGINAL PROBLEM STATEMENTS (UNLESS INDICATED OTHERWISE BELOW).

NOTE - BECAUSE MOST ANSWERS ARE PROVIDED, IT IS VERY IMPORTANT THAT YOU SHOW ALL STEPS IN YOUR WORK.  THE GRADING WILL BE BASED ON THE COMPLETENESS, CLARITY, AND CORRECTNESS OF YOUR WORK, NOT JUST THE ANSWERS YOU PROVIDE.

PLEASE BOX YOUR ANSWERS (EITHER BY HAND OR USING MATHCAD'S RESULT PROPERTIES FEATURES)
ON THIS AND EVERY FUTURE ASSIGNMENT.

9.1
[10 pts]
  • do this problem by hand (i.e., don't use MathCAD or any other software), and show your work (e.g., with matrix multiplication)
  • no answers are provided
  • See PT3.2 for the definition of the matrix transpose.
9.3
[20 pts]
  • do this problem by hand, and show your work
  • no answers are provided
  • see PT3.2 for definitions, notation, and examples
  • Some operations in part d may not be possible. If this is the case, indicate so and explain why.
  • In items 11 and 12 in d, multiplication is implied (the "x" is not required to indicate multiplication). Show your work for at least two of the elements of the result to demonstrate you know how to do the matrix multiplication calculations manually.
  • Please make sure you solve the entire problem (through d-12).
9.6
[20 pts]
  • do this problem by hand and show all steps
  • also solve in MathCAD using a matrix inverse
  • x1 = -2, x2 = 8, x3 = -3
9.12
[25 pts]
  • do this by hand and show all steps, as demonstrated in class
  • use basic Gauss-Jordan elimination only (i.e., do not use any sort of pivoting).
  • also solve in MathCAD using a matrix inverse
  • x1 = 14, x2 = -32, x3 = -5
S5
[25 pts]

NOTE - this problem is not in the book.

  • Using each of the methods described below, solve the following set of two equations:
    • 2y = (x-1)2 + 1
    • sin(x) = y
  • DO NOT substitute one equation into the other to reduce the problem to one equation
  • (a) determine solution estimates by plotting functions in MathCAD
  • (b) use a MathCAD given-find solve block with an initial guess of (x, y) = (1.4, 0.75)
  • (c) use 5 iterations of the Newton-Raphson technique with an initial guess of (x, y) = (1.4, 0.75). Show the values for all iterations. After 5 iterations, (x, y) = (1.933, 0.935).
  • (d) test the validity of the solution from step (c)