I have a homework at linear algebra and we have this system of linear equations:
$ x+y+z+w=0 $
$ x+2*y+9*z+13*w=0 $
$4*x+41*y+6*z+656*w = 0 $
And we add this equation:
$ x^3 + y^4 + 8* z^5 + 8* w^6 = 0 $
What can be said about the solution set of this system?
- w~~0, x~~0, y~~0, z~~0
- w~~-0.0417376, x~~-0.665814, y~~0.73708, z~~-0.0295286
Doesn't this mean that the solution set is a non empty set?
And also that it is a finite set (with 2 elements? the (0,0,0,0) and (-0.0417376, -0.665814, 0.73708, -0.0295286) ?
Also, how can I find out if the solution set of the above system is a vector space?