1.2 Matrices Vectors and

Gauss – Jordan elimination

(This is such an interesting topic that it was made into a

movie)

Matrix Notations

A website that has programs that will do most operations in this course (an online calculator for matrices)http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi

Write the system as a matrixWrite 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

Solution

Solution slide 2

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.)

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 columnStep 3: Get a 1 on the main diagonal in the next

column.Step 4: Get zeros below the one obtained in step 3Step 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.

Reduced Row-Echelon (rref) Form

A matrix is in reduced-row echelon form if it satisfies all of the following conditions:

a) If a row has nonzero entries, then the first nonzero entry is 1 called the leading 1 in this row.

b) If a column contains a leading 1, then all other entries in that column are zero

c) If a row contains a leading 1, then each row above contains a leading 1 further to the left

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?

Write the given matrix in reduced row echelon form using a TI-89

Calculator2nd 5 (math)

4 (matrix)

4(rref) - rref stands for reduced row echelon form

rref([1,3;2,5])

Homeworkp. 18 1-19 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...'