Math 3280 - Hampton - Lab 4- Due 6/26

An introduction to matrices with Mathematica.

Exercises

Matrices in Mathematica are just lists: lists of lists of entries. There are many built-in matrix commands such as RowReduce and Inverse. The operation of matrix multiplication is represented with a period, e.g.to multiply matrix A times matrix B,we input "A.B" (without the quotes).

The command MatrixForm is useful for inspecting matrices.

1. Verify that the inverse of the matrix product AB, (AB)^(-1), is the inverse of B times the inverse of A (i.e. B^(-1)A^(-1)) in the particular case A = {{3,5,4}, {4,7,5}, {5,9,7}}, B = 
{{1,0,3},{0,30,0},{1,0,2}}, by computing with Mathematica.

2.  Use the Solve command to find a complete solution to the worksheet 7 problem: what are the two by two matrices A = {{a,b},{c,d}} such that A times A=I (the identity)? 

3.  A customer at a paint store orders 81 gallons of paint that contains equal amounts of red, blue, and white paint.  However, the store wishes to prepare this order by mixing three types of paint that they already have on hand:
	* a reddish paint with 50% red, 25% blue, and 25% white paint
	* a bluish paint with 12.5% red, 75% blue, and 12.5% white paint
	* a pale purple paint with 20% red, 20% blue, and 60% white paint.
How many gallons of each are needed to fulfill the customer's order?