Solve the linear system {x + y - z = 1 x + y + z = 3 x - y = 4. Solve the linear

Question

Solve the linear system {x + y - z = 1 x + y + z = 3 x - y = 4. Solve the linear system {x + y - z = 1 x + y + z = 3. Express your solutions in parametric form. Show that the linear system x + y - z = 1 x + 2y + 3z = 4 2x + 3y + 2z = 3 is inconsistent. Use Gaussian elimination to solve the system {x_1 + 2x_2 - 3x_3 + 4x_4 - 5x_5 = 6 x_1 - x_2 + x_4 - 2x_5 = 0 x_1 + x_3 - x_5 = 2. Write your solution in parametric form and show all your work. Use the Gauss-Jordan method to solve the system {x + 3y = 1 2x + 7y = 3. Show all your work.

Explanation / Answer

1)

x+y -z = 1 --------------------1

x+y+z = 3 ---------------------2

x -y = 4 ------------------------3

eqn 2 - eqn 1

(x+y+z) - (x+y-z) = 3 - 1

2z = 2 ; z = 1

eqn 1 + eqn 3

(x+y-z) + (x-y) = 1+ 4

2x - z = 5

2x -1 = 5 ; 2x = 6 ; x = 3

On Putting values of x and z in eqn 2

x+ y + z = 3

3+y+1 = 3

y = -1

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