Give a geometric comparison of the solutions to x1 3x2 5x3

Give a geometric comparison of the solutions to x_1 + 3x_2 -5x_3 = 4 x_1 +3x_2 -5x_3 = 0 x_1 +4x_2 -8x_3 = 7 and x_1 +4x_2 -8x_3 = 0 -3x_1 -7x_2 +9x_3 = -6 - 3x_1 -7x_2 +9x_3 = 0

Solution

First system is a non-homogeneous system.

It represents a plane not passing through the origin.

Second system is a homogeneous system.

It represents a plane passing through the origin.