Question

Solve the system of equations using matrices. Use Gaussian elimination with back-substitution. x + y + z = -5 x - y + 3z = -1 4x + y + z = -2

Answer 1

x + y + z = -5
x - y + 3z = -1
4x + y + z = -2

let's get rid of all the y's.

add these two equations...

x + y + z = -5
+ x - y + 3z = -1
--------------------------
2x + 4z = -6
2x = -6 - 4z
x = -2z -3

then add the last two equations..
x - y + 3z = -1
+ 4x + y + z = -2

5x + 4z = -3
4z = -5x -3
z = -5/4 - 3/4

substitute x = -2z -3 to any of the equations
-2z - 3 + y + z = -5
-z - 3 + y = -5
y = -2 + z