# Use Gaussian elimination with back substitution?

1. Jul 17, 2014

### Math10

Use Gaussian elimination with back substitution to solve the following system:

x1+x2+x3=1,
x1+2x2+2x3=1,
x1+2x2+3x3=1.

The answer is (1, 0, 0) and I know how to solve the problem but I just don't know if I should use bracket or the big parentheses for this type of problem when I solve this problem. Can anyone please provide me the work for this problem? Like do I use equal sign between the two bracket matrixes?

2. Jul 17, 2014

### WWGD

I think if you show us a scanned image of your work, we can better understand/help you. Brackets are usually used to denote determinants, parentheses are used for matrices.

3. Jul 17, 2014

If you are to use Gaussian elimination you set up the augmented matrix. Whether you write the matrix as
$$\begin{pmatrix} 1 & 1 & 1 & 1 \\ 1 & 2 & 2 & 1 \\ 1 & 2 & 3 & 1 \end{pmatrix}$$

or
$$\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & 2 & 2 & 1 \\ 1 & 2 & 3 & 1 \end{bmatrix}$$

is immaterial: some books use the first version, some the second. The thing in common is that (when you write by hand or see them in texts) there is typically a solid or dashed vertical line immediately before the final column (the line goes where the equal signs would be). That is used as a visual reminder that the numbers to the left are coefficients of equations while those to the right are the constants from the equations' right sides. Once you have the matrix set up you do the Guassian elimination work (which you need to do).

4. Jul 17, 2014

### Math10

Thank you, guys. I appreciated.