Use Gauss-Jordan elimination to solve linear systems. Do simple problems using paper and pencil, and use technology to solve more complicated problems. In Exercises 1 through 12, find all solutions of the equations with paper and pencil using Gauss-Jordan elimination. Show all your work. Solve the system in Exercise 8 for the variables x_1, x_2, x_3, x_4, and x_5. |x + y - 2z = 5 2x + 3y + 4z = 2| |3x + 4y - z = 8 6x + 8y - 2z = 3| x + 2y + 3z = 4 |x + y = 1 2x - y = 5 3x + 4y = 2| |x_3 + x_4 = 0 x_2 + x_3 = 0 x_1 + x_2 = 0 x_1 + x_4 = 0| x_1 - 7x_2 + x_5 = 3 x_3 - 2x_5 = 2 x_4 + x_5 = 1| |x_1 + 2x_2 2x_4 + 3x_5 = 0 x_3 + 3x_4 + 2x_5 = 0 x_3 + 4x_4 - x_5 = 0 x_5 = 0| |x_2 + 2x_4 + 3x_5 = 0 4x_4 + 8x_5 = 0| |x_4 + 2x_5 - x_6 = 2 x_1 + 2x_2 + x_5 - x_6 = 0 x_1 + 2x_2 + 2x_3 - x_5 + x_6 = 2| |4x_1 + 3x_2 + 2x_3 - x_4 = 4 5x_1 + 4x_2 + 3x_3 - x_4 = 4 -2x_1 - 2x_2 - x_3 + 2x_4 = -3 11x_1 + 6x_2 + 4x_3 + x_4 = 11| |x_1 + 2x_3 + 4x_4 = -8 x_2 - 3x_3 - x_4 = 6 3x_1 + 4x_2 - 6x_3 + 8x_4 = 0 - x_2 + 3x_3 + 4x_4 = -12|