# Some Maple Warmup Problems (Math 221 Version)

1. Use Maple to calculate A3 v1 + 3 v2 where

2. Let A be the matrix

Calculate A100,A200, and A300. Compare.

3. Use the row operations package to solve the system of linear equations:

( Samples using the row operations package are located in the file :Maple V Release 4:Math 221: Row Operations Examples on each Macintosh. )

4. Now use Use Maple's solve command on the above system. (This is easier, but probably less instructive ....) There is also a linsolve command in Maple which could also do this in one step.

5. For each of the following matrices A, describe all 2 x 2 matrices B so that A B - B A = 0:

a)

b)

c)

d)

e)

HINT: If U is a matrix of expressions in variables {a,b,c,d}, then solve(convert(U,set),{a,b,c,d}) will generate the solutions to the matrix system U=0.