1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
erastova [34]
3 years ago
6

Use Gauss-Jordan row reduction to solve the given system of equations. HINT [See Examples 1-6.] (If there is no solution, enter

NO SOLUTION. If the system is dependent, express your answer in terms of x, where y = y(x) and z = z(x).) − 1 2 x + y − 1 2 z = 0 − 1 2 x − 1 2 y + z = 0 x − 1 2 y − 1 2 z = 0
Mathematics
1 answer:
Effectus [21]3 years ago
8 0

Answer:

x = 0, y = 0, z= 0

Step-by-step explanation:

The idea of Gauss Jordan row reduction is to reduce the matrix form of the system of equation to reduced row echelon form using some elementary row operations. There are three operations that can be performed on the rows, namely;

1. swap two rows.

2. multiply one row by a nonzero number

3. add or substract the multiple of one row to/from another

For the given exercise, the matrix form is given as

\left[\begin{array}{cccc} -12&1&-12 & 0\\-12&-12&1 & 0\\1&-12&-12&0\end{array}\right]

These are the operations that are performed to get the reduced row echelon form.

1. swap Row1 and Row3

\left[\begin{array}{cccc} 1&-12&-12 & 0\\-12&-12&1 & 0\\-12&1&-12&0\end{array}\right]

2. Row2 + 12*Row1 and Row3 + 12*Row1

\left[\begin{array}{cccc} 1&-12&-12 & 0\\0&-156&-143 & 0\\0&-143&-156&0\end{array}\right]

3. -1/156 * Row2

\left[\begin{array}{cccc} 1&-12&-12 & 0\\0&1&143/156 & 0\\0&-143&-156&0\end{array}\right]

4. Row1 + 12*Row2 and Row3 + 143*Row2

\left[\begin{array}{cccc} 1&0&-1 & 0\\0&1&143/156 & 0\\0&0&-3837/156&0\end{array}\right]

5. -156/3837 * Row3

\left[\begin{array}{cccc} 1&0&-1 & 0\\0&1&143/156 & 0\\0&0&1&0\end{array}\right]

6. Row1 + Row3

\left[\begin{array}{cccc} 1&0&0 & 0\\0&1&143/156 & 0\\0&0&1&0\end{array}\right]

The matrix is now reduced to the row echelon form.

From Row1, the element in the first column is equal to 1 and the last column is equal to zero, this implies that x = 0.

From Row2, the element in the second column is equal to 1, the third column is equal to 143/156 and last column is zero, this means that y + 143/156 z = 0

Similarly from Row3, z = 0.

Putting these together, x = 0, y = 0, z= 0

You might be interested in
Use the sample data and confidence level to construct the confidence interval estimate of the population proportion p. n=500, x=
DiKsa [7]

Answer:

0.3581<x<0.4429

Step-by-step explanation:

Using the formula for calculating the confidence interval of the population proportion p expressed as:

Confidence interval = p ± Z * √p(1-p)/n

p is the population proportion = x/n

p = 200/500

p = 0.4

Z is the z-score at 95% CI = 1.96

n is the sample size = 500

Substituting the given parameters into the formula we will have;

Confidence interval = 0.4 ± 1.96 * √p(1-p)/n

Confidence interval = 0.4 ± 1.96 * √0.4(0.6)/500

Confidence interval = 0.4 ± 1.96 * √0.24/500

Confidence interval = 0.4 ± 1.96 * √0.00048

Confidence interval = 0.4 ± 1.96 * 0.0219

Confidence interval = 0.4±0.04294

Confidence interval = (0.3571, 0.4429)

Hence the confidence interval of the population mean is 0.3581<x<0.4429

5 0
3 years ago
Quick Answers Please
Rudik [331]

Then Nicolas would have:

4 and 1/16 of that one pizza

8 0
3 years ago
6. To clean his floors, Larry uses a recipe for a homemade cleaner of 1 part lemon juice, 1 part vinegar,
Katarina [22]
8 cups lemon juice
8 cups vinegar
16 cups hot water
6 0
3 years ago
60=F(15) <br><br> Please solve this and show work, please
Lubov Fominskaja [6]

Answer:

f = 4

Step-by-step explanation:

60= 15f

divide both side by 15

f = 4

3 0
3 years ago
Plz help me I am timed! Well mark brainliest if you are correct!
omeli [17]

Answer:

A

Step-by-step explanation:

The point Y is the center of the circle

6 0
2 years ago
Read 2 more answers
Other questions:
  • Write an inequality for the following statement.<br> 9 is greater than a
    10·2 answers
  • How much is 20 x 20?
    14·2 answers
  • Mrs. Ameldo's class has 5 students with blue eyes, 7 with brown eyes, 4 with hazel eyes, and 4 with green eyes. Two students are
    11·2 answers
  • Find the quadratic polynomial if zeros of it are 2 and 1/3 respectively​
    13·1 answer
  • Solve the system of equations using the substitution method.
    12·1 answer
  • What is the volume of the pyramid in cubic inches?
    5·1 answer
  • Determine the value of c that will result in a perfect square trinomial. <br> w^2+6w+ c =130+c
    13·1 answer
  • Pls help me with this true or false question
    5·2 answers
  • I WILL GIVE BRAINLY IF UR RIGHT
    9·2 answers
  • A square with the length of 12 millimeters. The area of the square is marked as 132 square millimeters. find the perimeter
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!