Dr. Sarah's Linear Algebra Commands for Maple for Chapter 2 (See also PS 1 Hints)
> restart: with(LinearAlgebra):
Inverse of a Matrix
Maple can find the inverse of a matrix a lot quicker than we can by hand! We did 2.3 number 10 via the Gauss-Jordan method. Now let's do it on Maple:
Check your notes to see that this is the same answer that we got in class via the Gauss-Jordan method of finding an inverse. Note that on p. 151, Lamp has 2 methods of constructing the inverse, but the Inverse(A); command requires with(Lamp): in addition to with(LinearAlgebra):
Product of Two Matrices
To find the product of two matrices, first we define the matrices, and then use Maple's command to multiply which is a period. Be sure to use Matrix and not matrix in your definition (see A above).
Let's check that A and B from above are really inverses of each other:
> A.B; B.A;
So they really are inverses. See p. 112 LAMP for another example of multiplication of two matrices defined from scratch.
LAMP Markov Chain of Planes at Three Hubs - Problem 4 p. 147
You may wish to review LAMP Chapter 3 Module 4.
PART A: We'll start by letting
Notice that MN = N2=
Use this information and your knowledge of matrix multiplication in order to solve for the entries of M (in decimal instead of percentage format). HINT: Note that a11 is NOT .02 because by matrix multiplication, the first entry in MN must equal the first entry in N2 and so
In order to make the units match correctly, we see that a11 must be the percentage of planes that start in Seattle and end up in Seattle.
Use a similar reasoning to determine M. Then define M:=Matrix([[... using the Maple Matrix command.
PART B: After you have defined M, then you can execute the command
> for k from 5 to 200 by 40 do M^k end do;
Use your understanding from LAMP module Chapter 3 Module 4 in order to answer part b.