Question

Row Echelon/Guassian Elimination question.

Answer 1

I have a 3x3 matrix and I was trying to put it into Row Echelon form. Now the book says this:

1. If a row does not consist entirely of zeros, then the first nonzero number in the row is a 1. We call this a leading 1.
2. If there are any rows that consist entirely of zeros, then they are grouped together at the bottom of the matrix.
3. In any two successive rows that do not consist entirely of zeros, the leading 1 in the lower row occurs farther to the
right than the leading 1 in the higher row

Answer 2

I knew that everything has to have leading 1's, but for some reason this matrix is giving me an issue...

http://www.wolframalpha.com/input/?i=determinant+of+%7B%7B3%2C-6%2C9%7D%2C%7B-2%2C7%2C-2%7D%2C%7B0%2C1%2C5%7D%7D

this is what I went for

http://www.wolframalpha.com/input/?i=determinant+of+%7B%7B1%2C-2%2C3%7D%2C%7B0%2C1%2C5%7D%2C%7B1%2C%28-7%2F2%29%2C1%7D%7D

I am using a program called Maple, and it shows us how to do the Guassian/Guass-Jordan methods, but for some reason this seems off...
http://www.wolframalpha.com/input/?i=determinant+of+%7B%7B3%2C-6%2C9%7D%2C%7B0%2C3%2C4%7D%2C%7B0%2C0%2C%2811%2F3%29%7D%7D


Now it says it's supposed to have 1's all along the diagonal, so why is there no 1's in this answer? I'm very confused...

Answer 3

What does your matrix look like? Maybe I can step you through it.

Answer 4

First link cliff.

Answer 5

second is my attempted(since it's supposed to having leading 1's)

third link is the actual answer for some odd reason...

Answer 6

Right, sorry, the page took a while to load. I see it now.

Answer 7

:)

Answer 8

Er, yeah, that does look strange.
For row-echelon you want the bottom triangle to be zeros. For reduced-row-echelon, you want 1's along the diagonal.

It's a square matrix though, so one of your rows will likely go to all zeros.

Answer 9

I noticed that it wants 0's but 3's? WUUUT...?

Answer 10

are you trying to get row echelon or the determinant?

Answer 11

The 3's are ok.

Answer 12

evaluate the determinant of the given matrix by reducing the matrix to row echelon form.

Answer 13

Why is that cliff? In my book they showed everything being ones... and it say sleading 1.

Answer 14

so that really means nothing for row reducing huh...

Answer 15

ah so in other words itwants you to get a diagonal

Answer 16

basically make a lower right triangle

Answer 17

>( I don't wanna.

Answer 18

and then what that says is when you have a lower triangle. the determinant is the diagonal

Answer 19

You can make the 3's into 1's if you wanted to. It would probably make computing the determinant slightly easier.

Answer 20

\[\left[\begin{array}{ccc} 3&-6&9\\-2&7&-2\\0&1&5\end{array}\right]\]

Answer 21

But I don't HAVE TO HAVE 1's.. Only for reduced row echelon ...

Answer 22

row echelon is this