# Alg 2 - Math

need help with hw...

Use Gauss-Jordan to solve

3x – 2y + z = 6

3x + y – z = -4

-x + 2y – 2z = -8

1. 👍
2. 👎
3. 👁
1. Start by transcribing the equations to a 3x4 matrix
3 -2 1 6
3 1 -1 -4
-1 2 -2 -8
The first step is to reduce each column to zero (except the diagonal element and above) by linear combination of rows. I'll do the first one:
3 -2 1 6
0 3 -2 -10 (row 2 - row 1)
0 4 -5 -18 (3*row 3 + row 1)
Continue:
3 -2 1 6
0 3 -2 -10
0 0 7 14 (4*row 2 - 3*row 3)
The last row can be simplified:
3 -2 1 6
0 3 -2 -10
0 0 1 2
So z=2, substitute z=2 in row 2 to eliminate elements above the diagonal
3 -2 0 4 (row 1 - row 3)
0 3 0 -6 (row 2 + 2*row 3)
0 0 1 2
Simplify row 2:
3 -2 0 4
0 1 0 -2 (row 2/3)
0 0 1 2
Now eliminate column 2 from row 1
3 0 0 0 (row 1 + 2*row 2)
0 1 0 -2
0 0 1 2
So
x=0
y=-2
z=2

1. 👍
2. 👎

## Similar Questions

1. ### biology

jordan is doing a science fair project on the effect of music on the growth of tomatoes. he has two tomato plants, plant A and B, that he grows in a window and gives the same amount of water. plant A is exposed to classical music

2. ### Language Arts

3. In "All Together Now," Jordan uses appeals to emotion and appeals to reason to try to persuade her readers that her views are important. In a paragraph, cite one example of each kind of appeal in her work. Then, explain whether

3. ### History

How are the governments of Jordan and Kuwait different from the governments of the United Arab Emirates and Oman? A. Citizens of Jordan and Kuwait can vote. B. Jordan and Kuwait have monarchs. C. The king of Jordan and emir of

4. ### Gauss jordan elimination

Use Gauss - jordan elimination to solve for the values of the unknown. x + y-z = 20 2x + 3y -z = 15 3x -5y + 2z = 10

1. ### LA

In "All Together Now," Jordan uses appeals to emotion and appeals to reason to try to persuade her readers that her views are important. In a paragraph, cite one example of each kind of appeal in her work. Then, explain whether

2. ### Physics

Michael Jordan, formerly of the Chicago Bulls basketball team, has some fanatic fans. They claim that he is able to jump and remain in the air for two full seconds from launch to landing. Evaluate this claim by calculating the

3. ### algebra

Jordan and Missy are stnading together in the schoolyard. Jordan, who is 6 feet tall, casts a shadow that is 54 inches long. At the same time, Missy casts a shadow that is 45 inches lobg. How tall is missing? 1 38in 2 86.5in 3 5ft

4. ### linear algebra

solve using gauss jordan 10y − 4z + w = 1 x + 4y − z + w = 2 3x + 2y + z + 2w = 5 −2x − 8y + 2z − 2w = −4 x − 6y + 3z = 1

1. ### Math

Jordan has 4/5 as many DVDs as Joseph. If Jordan has 56 DVDs, then how many does Joseph have? Please help my brain is mush

2. ### English

In "All Together Now", Jordan uses appeals to emotion and appeals to reason to try to persuade her readers that her views are important. In a paragraph, cite one example of each kind of appeal in her work. Then, explain whether

3. ### math 6

Jordan has as many DVDs as Joseph. If Jordan has 56 DVDs, then how many does Joseph have? 4/5 x 56/1 = 224/5 = 44.40 answer 44 DVD's Is all this correct?

4. ### Linear Algebra

Use the Gauss-Jordan method to find all the solutions of the system -3x1 +2x2 -x3 +6x4 = -7 7x1 -3x2 +2x3 -11x4 = 14 x1 -x4 = 1 It is a 3x5 matrix -3 2 -3 6 -7 7 -3 2 -11 14 1 0 0 -1 1 Using the Gauss-Jordan method, I got 1 0 0 -1