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- The matrix below expresses the approximate distance, in miles,
between any of the following two cities: Houston, Los Angeles, New York, and
Washington DC.
- What special kind of matrix is this (other than square and 4 by 4)?
- If we want to know the same information in kilometers, what should we
do? Remember, for our purposes here, one mile is equal to 1.6 kilometers.
- What is the resulting matrix when you perform the operation that you suggested in part (b)?
- Perform the operations requested below if they are possible using
these matrices.
- 4C
- AD
- DA
- BC
- 3CB
- C (A + B)
- AB
- BA
- CAD
- DBC
- AD + (CB)T
- DC
- CD
- The matrix G represents the average score for each student on
tests, quizzes, and homework. Tests are 50% of the grade, quizzes are 30%
and homework is 20%.
- Write the vector P expressing the percentages that would be used to find the final grade for each student.
- Would GP or PG produce a matrix of the final grades?
- Using matrices, determine the final grade for each student. Please show your work.
- Does c(Ax) = A(cx) where c is a scalar, A is a 2 by 2 matrix, and x is a dimension 2 column vector? Explain your answer.
- Place the parentheses where needed to minimize the
number of multiplications performed to work this problem. How many simple
multiplications did it take to find T?
- Does
satisfy the equation
Explain why A does or does not satisfy the equation.
Note: For real numbers, a multiplied by itself n times can be written as an.
Similarly, the matrix A multiplied by itself n times can be written as An. Therefore, A2 means AA.
Computer Program
Make changes and additions to your program from Chapter 2 so that it can
also multiply matrices. A warning message should be displayed if the
matrices are not of correct dimensions for the operation requested. Your
program should be able to handle (AB - C + D)E and other similar problems.
Remember that your program should be user-friendly and should have comments
in the code. Again, write this program without using any commands that
directly read, write, or manipulate matrices.
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