# Thread: Need help solving equations from this matrix

1. ## Need help solving equations from this matrix

I have a matrix

1 0 5 0 0
0 1 1 5 0
0 0 0 0 1

Which gives the three equations:

X1 + 5X3 = 0
X2 + X3 + 5X4 = 0
4X5 = 0

Now in my notes it says that you can solve it to get:

X1 = 2X3 + 0X4
X2 = 6X3 + 2X4
X3 = 1X3 + 0X4
X4 = 0X3 + 1X4
X5 = 0X3 + 0X4

Could someone help explain to me how you go from the first equations to the second, for the life of me i can't figure it out

2. I've been looking at this for a while myself..!

I am no genius, but are you sure you are looking on the right notes?

How can $x_1 + 5x_3 = 0$ go to $x_1 = 2x_3$, unless $x_3 = 0$ I guess?

3. Yeah i just double checked the notes, that's exactly what it says. And there not my notes either there the lecturers.

Can't understand what's happening and he dosen't explain it anywhere, it's to do with finding the complete solution to this system of linear equations.
Where these two are matricies.

4 2 1 3 6 ......4
0 3 3 1 0.x.=..6
3 2 4 1 5 ......2

over $Z7$

Firstly he applies GJ to the whole lot in one matrix to get:

1 0 5 0 0 3
0 1 1 5 0 2
0 0 0 0 1 2

Then he splits the matrix into to and gets:

......3
......2
G....0
......0
......2

1 0 5 0 0
0 1 1 5 0....=....0
0 0 0 0 1

Then he solves to get the equations listed above

4. Originally Posted by BigBoss22
I have a matrix

1 0 5 0 0
0 1 1 5 0
0 0 0 0 1

Which gives the three equations:

X1 + 5X3 = 0
X2 + X3 + 5X4 = 0
4X5 = 0

Now in my notes it says that you can solve it to get:

X1 = 2X3 + 0X4
From the first equation above, X1= -5X3, not 2X3

X2 = 6X3 + 2X4
and X2= -X3- 5X4, not 6X3+ 2X4

X3 = 1X3 + 0X4
X4 = 0X3 + 1X4
X5 = 0X3 + 0X4
The last equation in the set clearly says that X5= 0.

Could someone help explain to me how you go from the first equations to the second, for the life of me i can't figure it out