MATH 3191 Spring 1999 Bennethum
Projects

Each of the following projects are worth 10 points extra credit towards your homework. In order to get an A in the course, you must do at least one project. All projects are due 2 weeks after the homework from that section is due.

1. (Section 2.8) Make up a 2-dimensional figure which can be constructed from a set of 8 or more points (as in text, Figure 2 of the letter N). Consider exercise 12 p. 163. We want to rotate your figure 75 degrees counter-clockwise.
1. Using a computer/calculator to calculate each matrix multiplication, rotate it by first multiplying the homogeneous coordinates by each matrix given in problem 12 successively. After each matrix multiplication plot the new set of points (by hand or with help of computer) and re-draw the picture. Turn in 4 pictures (the original, and the 3 new ones).
2.  Compute (use technology) the product of the three matrices and turn in the resulting matrix.
3.  Check your answer in part (a) by multiplying your homogeneous coordinates by the matrix in (b).
2. (Section 3.3) Determine the inverse of matrix A in three ways:




1. Using Cramer's Rule (all programs which have some matrix capability are capable of determining the determinant; however very few are capable of calculating adj(A) because it is very time-consuming to do so. In order to calculate the adj(A) you may write yourself a small computer code, or do a combination of hand and computer calculations. You need to mention how you calculate the adj(A) and write down the result. There is no need to turn in detailed calculations.
2.  Using LU decomposition. Find the matrices L and U and then the inverse of each of these matrices, then put together appropriately to find the inverse of A.
3.  Using your software. Tell me which software package you are using.
For each of the above methods, calculate  to get an idea of the error (no method will be exact due to computer round-off). Then write a couple of paragraphs comparing these methods - which method was the most accurate (or are they very similar?). How long does it take to compute the inverse? Can you explain this?
3. (Section 6.6) Problems 11 and 12. You must use a computer or calculator.
4.  (Your Own Project) If you have a linear algebra problem you are interested in studying from your job or from another class, or one that you saw in the text which interests you, you may propose to do that project as well. You will need to discuss it with me to be sure it is appropriate and at the right level of difficulty (it is actually very easy to come across a problem which is difficult to solve!). The requirements are that it must use topics developed in this course and it must be solved using a computer/calculator.

 

 

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Mon Feb 15 19:40:50 MST 1999