Matrix

MTH 111 - May 27, 2009

1. Today we will . . .
- do more arithmetic with matrices (6.4)
- start Section 6.5 (inverse of a matrix), if time
- take HW Quiz over 5.5, 6.1, 6.3

2. Your next test (your LAST midterm!!) is Monday
Will cover 2.6, 5.6, 6.1 - 6.5

Why do we multiply matrices the way we do?

EXAMPLE: Suppose that a custom de sign for a special event is
printed on a variety of tee shirts: long sleeved, short sleeved, and
tank top. And suppose that sales of these tee shirts for two
different years were:

(a) What does the sum A + B represent?
(b) What does the difference B - A represent?
(c) What does the scalar multiple 2A represent?

And what about multiplication?

Suppose that LS tee shirts sold for $20, SS sold for $12, and TT
sold for $10 in 2007.

What was the revenue from each size of shirt? We can find this
using matrix multiplication. But first we must make a new matrix.

One very special matrix in terms of multiplication is the identity
matrix. Here's the identity matrix for 2 x 2 matrices

Let's see why it's special.

How do matrix operations relate to systems of equations ?

It turns out every system of equations can be re presented by a matrix
equation. Here's how it works using the system of equations we
solved earlier .

Sec 6.5: The Inverse of a Matrix

We have performed row ope rations to solve a system of equations using
matrices. But there is another method that works much faster IF the
system of equations has just one solution .

But first we need to talk about the inverse of a matrix.

What do we do to solve this equation? 2x = 10