help with this matrix!!?

Question

the augmented matrix:

1 0 2 4 5
0 1 0 1 -2
0 0 0 1 3
0 0 -2 0 6

what is the next pivot????

Answer 1

[ 1 0 2 4 5 ]
[ 0 1 0 1 -2 ]
[ 0 0 0 1 3 ]
[0 0 -2 0 6 ]

Your next step would be to swap the 3rd and 4th row.

R3 <--> R4

[ 1 0 2 4 5 ]
[ 0 1 0 1 -2 ]
[0 0 -2 0 6 ]
[ 0 0 0 1 3 ]

You can probably take it from here, but in case you cannot,

R3 -> (-1/2) R3

[ 1 0 2 4 5 ]
[ 0 1 0 1 -2 ]
[0 0 1 0 -3 ]
[ 0 0 0 1 3 ]

Answer 2

Add first and last to get

1 0 0 4 11

Now add this to 3rd line (*(-4)) to get

1 0 0 0 -1

Also add 2nd to 3rd (*(-1)) to get

0 1 0 0 -5

Transpose 3rd and 4th (after multiplying 4th by -1/2)

1 0 0 0 -1
0 1 0 0 -5
0 0 1 0 -3
0 0 0 1 3

Does that do the trick?