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 go to , unless I guess?
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
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
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
From the first equation above, X1= -5X3, not 2X3
and X2= -X3- 5X4, not 6X3+ 2X4X2 = 6X3 + 2X4
The last equation in the set clearly says that X5= 0.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