Question

Matrix question is so confusing

Answer 1

The answer matrix is

$\left[\begin{array}{ccc}1 & -4 & 3\\0 & 1 & \frac{-9}{13}\end{array}\right]$

The top row's answer boxes are: 1,  -4,  3

(These values are the same as in the given matrix)

The bottom row's answer boxes are:  0, 1, -9/13

=======================================================

Explanation:

Row echelon form will have us turn the "3" into a 0. To do this, we multiply everything in row 1 by the value -3

Row 1 is initially: 1, -4, 3

Multiply that row by -3 to get: -3, 12, -9

Then add these values to the values in row 2 and we get:

-3+3 = 0

12+1 = 13

-9+0 = -9

These three sums replace what you see in row 2

This is the new matrix we have now

$\left[\begin{array}{ccc}1 & -4 & 3\\0 & 13 & -9\end{array}\right]$

Again the first row has not changed. Only the second row has been altered.

The next and last step is to turn that 13 into a 1. Recall we want the pivot positions to be 1. Divide everything in row 2 by 13 to get this accomplished.

0---> 0/13 = 0

13 ----> 13/13 = 1

-9 ---> -9/13

we now have

$\left[\begin{array}{ccc}1 & -4 & 3\\0 & 1 & \frac{-9}{13}\end{array}\right]$

We stop here since we don't need to get the matrix into reduced row echelon form (RREF) and instead only need to get it into row echelon form (REF). Throughout this whole process, row 1 has not changed.