Question

Use
Gaussian Elimination to solve and show all steps:

1. (x+4y=6)

(1/2x+1/3y=1/2)

2. (x-2y+3z=7)

(-3x+y+2z=-5)

(2x+2y+z=3)

Answer #1

Consider the following linear system:
x + 2y + 3z = 6
2x - 3y + 2z = 14
3x + y - z = -2
Use Gaussian Elimination with Partial Pivoting to
solve a solution in an approximated sense.

1. Solve by via Gauss-Jordan elimination:
a) 2y + 3z = 8
2x + 3y + z =
5
x − y − 2z =
−5
b) x + 3y + 2z = 5
x −
y + 3z = 3
3x + y + 8z = 10
c) 3x1 + x2 + x3 + 6x4 = 14
x1 − 2x2 +
5x3 − 5x4 = −7
4x1 + x2 + 2x3 + 7x4 =
17

Solve the following system of equations.
{−x+4y−z=-4
3x−y+2z=6
2x−3y+3z=−2
Give your answer as an ordered triple
(x,y,z).

Solve the system using 3x3
3x-2y+z=2
5x+y-2z=1
4x-3y+3z=7

Solve each system of equations
x-2y+3z=7
2x+y+z=4
-3x+2y-2z=-10

Solve by matrix method
x-y+2z=7
3x+4y-5z=-5
2x-y+3z=12

1. Solve the following system of equations by the elimination
method:
2x+y-z=7
x+2y+z=8
x-2y+3z=2
2. Solve the following system of equations by using row
operations on a matrix:
2x+y-z=7
x+2y+z=8
x-2y+3z=2

Use Gaussian elimination with backward substitution to solve the
system of linear equations.
x+y-z=-4
-x-4y+4z=1
-4x-3y+2z=15
What is the solution set?

#7 Solve for x, y and z
6x+3y+z=-27
x-3y+2z+10
17x-2y+3z=-65

Solve the sytem using elimination. Do not use augmentive
matrix.
(a) 3x - 2y + z = 2
(b) 5x + y - 2z = 1
(c) 4x - 3y + 3z = 7

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