# Answer to Question #15753 in Linear Algebra for samy

Question #15753

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

-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

Expert's answer

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.

| 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.

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