1. 1.2 Matrices Vectors and Gauss – Jordan elimination (This is such an interesting topic that it was made into a movie)

2. Matrix Notations
A website that has programs that will do most operations in this course (an online calculator for matrices)

3. Write the system as a matrix Write the following matrix in reduced row echelon form (example taken from p. 12 of text)
2x + 8y + 4z = 2
2x + 5y + z = 5
4x + 10y – z = 1

4. Solution

5. Solution slide 2

6. What are legal steps for reducing a matrix?
You are allowed to interchange rows.
You are allowed to multiply a row by a constant.
You are allowed to add two rows together.
(This implies that you can multiply a row by a constant then add it to another row.)

7. What is the order that a matrix should be simplified?
Step 1: Get a 1 in the upper left hand corner.
Step 2: Obtain 0’s for the rest of the first column
Step 3: Get a 1 on the main diagonal in the next column.
Step 4: Get zeros below the one obtained in step 3
Step 5: return to step 3 and repeat steps 3 and 4 until there are 1s on the main diagonal and zeros below it.
Step 6: start on the right most column and get zeros above the main diagonal. Repeat this for all diagonals from right to left.

8. Reduced Row-Echelon (rref) Form
A matrix is in reduced-row echelon form if it satisfies all of the following conditions:
If a row has nonzero entries, then the first nonzero entry is 1 called the leading 1 in this row.
If a column contains a leading 1, then all other entries in that column are zero
If a row contains a leading 1, then each row above contains a leading 1 further to the left

9. Which matrices are in Reduced Row Echelon form
Which matrices are in Reduced Row Echelon form? If a matrix is not in rref then what changes would be needed to change it to that form?

10. Write the given matrix in reduced row echelon form using a TI-89 Calculator
2nd 5 (math)
4 (matrix)
4(rref) - rref stands for reduced row echelon form
rref([1,3;2,5])

11. Homework
p odd,18, 20, 21, 22, 27
Q: How does a mathematician induce good behavior in her children? A: `I've told you n times, I've told you n+1 times...'