# System of linear equations

1. Oct 27, 2014

### princejan7

1. The problem statement, all variables and given/known data
I'm given a system of equations and I'm told to:
Solve this system by hand in 4-decimal digit arithmetic with rounding, using Gaussian elimination without
pivoting and backward substitution

2. Relevant equations

3. The attempt at a solution
When they say 'without backward substitution', what am I supposed to do instead?

2. Oct 27, 2014

### Staff: Mentor

I believe this means to completely reduce the matrix (reduced row-echelon form) so that the leading nonzero entry of each row is 1, and all entries above or below the 1 entry are 0.

In other words, it should look something like this:
$$\begin{bmatrix} 1 & 0 & ... & 0 & | & a \\ 0 & 1 & ... & 0 & | & b \\ . & . & ... & . &| . \\ 0 & 0 & ... & 1 & | & f \end{bmatrix}$$

Last edited: Oct 27, 2014
3. Oct 27, 2014

### Ray Vickson

If you use Gaussian elimination you cannot avoid using back substitution. However, if you use Gauss-Jordan elimination you avoid back substitution.