Solve the linear system by Gaussian Eliminatio method and determine whether the system is consistent or non consistent

Question

x-y+2z -w= -1

2x+y-2z-2w= -2

x + 2y-4z+ w= 1

3x-3w= -3

Answer 1

If a system is inconsistent, then no solution exists. If a point or set of points solve equations then

system is consistent,

start by eliminating w in first three equations (not exactly guassian) w=x+1

first equation provides y in terms of z

y=--2z

second equation x=2z,,,,,,,which also means w=2z+1

third equation using z only,

find z=0

meaning y=0

meaning x=0

meaning w=1

point (0,0,0,1)=(x,y,z,w) solves system