MATHEMATICS COLLEGE

The augmented matrix of a system of equations has been transformed to an equivalent matrix in​ row-echelon form. Using​ x, y, and z as​ variables, write the system of equations corresponding to the following matrix. If the system is​ consistent, solve it.left bracket Start 3 By 3 Matrix 1st Row 1st Column 1 2nd Column 2 3rd Column 2 2nd Row 1st Column 0 2nd Column 1 3rd Column negative 3 3rd Row 1st Column 0 2nd Column 0 3rd Column 1 EndMatrix Start 3 By 1 Table 1st Row 1st Column 4 2nd Row 1st Column 9 3rd Row 1st Column negative 2 EndTable right bracket

1 2 2
0 1 −3
0 0 1
4
9
−2
Which of the following system of equations corresponds to the given​ matrix?

A.

x plus 2 y plus 2 zx+2y+2z

equals=44

y minus 3 zy−3z

equals=99

z

equals=minus−22

B.

2 x plus 2 y2x+2y

equals=44

negative 3 y−3y

equals=99

z

equals=minus−22

C.

2 x plus 2 y plus 4 z2x+2y+4z

equals=1

negative 3 y plus 9 z−3y+9z

equals=1

minus−z

equals=1

D.

x

equals=44

2 x plus y2x+y

equals=99

2 x minus 3 y plus z2x−3y+z

equals=minus−22

Select the correct choice below and fill in any answer boxes in your choice.

A.

The solution set is

StartSet nothing EndSet{}.

​(Type an ordered​ triple.)

B.

The solution is the empty set.

Answers

Answer 1
Answer:

Answer: The system of equations is:

x + 2y + 2 = 4

y - 3z = 9

z = - 2

The solution is: x = -22; y = 15; z = -2;

Step-by-step explanation: ONe way of solving a system of equations is using the Gauss-Jordan Elimination.

The method consists in transforming the system into an augmented matrix, which is writing the system in form of a matrix and then into a RowEchelonForm, which satisfies the following conditions:

  • There is a row of all zeros at the bottom of the matrix;
  • The first non-zero element of any row is 1, which called leading role;
  • The leading row of the first row is to the right of the leading role of the previous row;

For this question, the matrix is a Row Echelon Form and is written as:

\left[\begin{array}{ccc}1&2&2\n0&1&3\n0&0&1\end{array}\right]\left[\begin{array}{ccc}4\n9\n-2\end{array}\right]

or in system form:

x + 2y + 2z = 4

       y + 3z = 9

               z = -2

Now, to determine the variables:

z = -2

y + 3(-2) = 9

y = 15

x + 30 - 4 = 4

x = - 22

The solution is (-22,15,-2).

Related Questions

Malik is buying a guinea pig. The guinea pig comes with a cage and food bowls for $ 125.00 . The expenses for feeding and caring for the guinea pig are $ 18.00 each month. How much will it cost Malik to buy and care for the guinea pig for one year?
What is the solution set for 4x - 6 < 6? {x:x > 3} {x:x < 3} {x:x < -1} {x:x >_ 3}
A mattress store sells only king, queen and twin-size mattresses. Sales records at the store indicate that the number of queen-size mattresses sold is one-fourth the number of king and twin-size mattresses combined. Records also indicate that three times as many king-size mattresses are sold as twin-size mattresses. Calculate the probability that the next mattress sold is either king or queen-size.
What is the greatest common factor shared by 40 and 20?Answer hereSUBMIT
Write a formula that will compute the final grade for the course, using G to represent the final grade, H to represent the homework average, Q to represent the quiz average, P to represent the project grade, T to represent the test average, and F to represent the final exam grade. Note: Keep in mind how you must write the percentages that show the weighting of each category when doing computations!

There are 16 entrees available at a restaurant. From these, Archie is to choose 6 for his party. How many groups of 6 entrees can he choose, assuming that the order of the entrees chosen does not matter ?

Answers

Answer: 8008

Step-by-step explanation:

Total entrees = 16

Number of entrees to choose = 6

Since order does not matter , so we combinations .

Number of combinations to choose r things out of n = C(n,r)=(n!)/(r!(n-r)!)

Then, total ways to choose 6 entrees = C(16,6)=(16!)/(6!10!)

=(16*15*14*13*12*11*10!)/((720)10!)\n\n= 8008

Hence, the required number of ways= 8008

Formula of simple intrest​

Answers

Formula : A = P (1 + r*t)

a - final amount

p- initial balance

r- interest rate

t- time

Find the slope of the line y=1

Answers

The Slope is 0. The graph will not rise or fall
True it will go across the positive 1 line on the y axis

F(x )= ?g(x) = ?
Neither function can be the identity function.
(There may be more than one correct answer.)

Answers

f(x) = {x}^(7)

g(x) = 3x + 3

_________________________________

f(x) = {x}^(14)

g(x) = √(3x + 3)

_________________________________

f(x) = ({5x - 10})^(7)

g(x) = (3)/(5)x + (13)/(5) \n

_________________________________

And many other answers....

The soccer team is making pizzas for a fundraiser. They put1/4 of a pound of cheese on each pizza. If they have 12 one-pound packages of cheese, how many pizzas can they make?

Answers

4 pizza equal 1 pound of cheese multiply 4×12=48

Which table represents the statement "Brian rides a bicycle at a rate of 12 meters per second"? Seconds /meters

Answers

Answer:

D

Step-by-step explanation:

The rate of 12 meters per second means that the constant of proportionality (k) or slope = 12.

That is m/s = 12.

The table that has a constant of proportionality that equals 12 is the table that represents the statement given.

The table in option D has a constant of proportionality of 12, since the ratio of m/s for all its given pair of values will give us 12 all through.

Answer:

I think your answer is B

Step-by-step explanation:
Other Questions
The solution of the equation x2-6x=0 is ?
To keep pace with a growing​ population, approximately​ _______ jobs must be created each month. A. ​100,000 B. ​137,000 C. 1 million D. ​185,000
A certain human red blood cell has a diameter of 0.000007 meters which expression represents this diameter in meters in scientific notation
Compact and oversized tires are produced on two different machines. The table shows the number of each type of tire produced, y, depending on the number of hours, x, the machines work.