Answer to Question #15753 in Linear Algebra for samy

Question

3x-3y+z=1
-x+3y+2z=-4
x+3y+5z=-7
for the above system of linear equations find a solution and show that it has infinitely many
solution or show that it has no soultion

Answer 1

Let's find the determinant of the given system:

| 3 -3& 1 |
|-1& 3& 2 | = 3*3*5 + (-1)*3*1 + (-3)*2*1 - 1*3*1 - 3*2*3 - (-3)*(-1)*5 = 0.
| 1& 3& 5 |

The determinant of the given system is zero, so this system has infinitely many solutions.