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charle [14.2K]
3 years ago
5

Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations. 2x+y+

z=-3 3x-5y+3z=-4 5x-y+2z=-2

Mathematics
1 answer:
Igoryamba3 years ago
3 0

Answer:

  (x, y, z) = (1, -1, -4)

Step-by-step explanation:

A suitable graphing or scientific calculator can find the reduced row-echelon form for you. There are on-line calculators that will do that, too.

_____

In general, if you want to do this by hand, you want to use row operations on the augmented matrix to make the diagonal elements 1 and the off-diagonal elements 0 as shown in the attached result.

If a[i,j] represents the element at row i, column j, you do that by dividing row i by a[i, i] (to make a[i, i] = 1), then subtracting the product of row i and a[k,i] from row k. (for all rows k ≠ i) For this 3-row matrix, repeat these steps for i = 1 to 3.

In the general case of an n by n+1 augmented matrix, you will be doing n^2 row operations, each one involving evaluation of n+1 expressions. The work rapidly grows with matrix size, so readily justifies use of a calculator.

As with many "elimination" problems, appropriate choice of sequence can reduce the work. The above algorithm always produces the reduced row-echelon form, but may result in messy arithmetic along the way.

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26. Students who take a statistics course are given a pre-test on the concepts and skills for the first chapter of a statistics
hjlf

The test statistic value lies to the right of the critical value. So we have sufficient evidence to reject the null hypothesis.

<h3>What are null hypotheses and alternative hypotheses?</h3>

In null hypotheses, there is no relationship between the two phenomenons under the assumption or it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.

Students who take a statistics course are given a pre-test on the concepts and skills for the first chapter of a statistics course.

Then they are given a post-test once the professor has concluded lecturing on the material.

Pre-test and post-test scores for 4 students in an elementary statistics class are given below.

Then we have

\mu _d = \mu _{post} - \mu _{pre}

Then the null hypotheses and alternative hypotheses will be

H₀: \mu _d = 0

Hₐ: \mu _d > 0

Then the test statistic will be

\rm \overline{x} _d = \dfrac{\Sigma x_d}{n} = \dfrac{15+12+10+1}{4}\\\\\overline{x} _d = 9.5

Then

\rm S_d = 6.02

The test statistic value is given by

\rm t = \dfrac{\overline{x} _d }{\dfrac{S_d}{\sqrtn}} \\\\t = \dfrac{9.5}{\dfrac{6.02}{\sqrt4}}\\\\t = 3.16

Since this is a right-tailed test, so the critical value is given by

\rm t_{n-1}(\alpha ) = t_3 (0.05) = 2.353

Since the test statistic value lies to the right of the critical value. So we have sufficient evidence to reject the null hypothesis.

Hence, we can conclude that \mu _d > 0 that is test scores have improved.

More about the null hypotheses and alternative hypotheses link is given below.

brainly.com/question/9504281

#SPJ1

7 0
2 years ago
Solve the following equation for the variable indicated<br> 15 = Зn + 6р, for n
Taya2010 [7]

Answer:

Solving the equation 15 = 3n + 6p for variable n we get \mathbf{n=5-2p}

Step-by-step explanation:

We need to solve the equation 15 = 3n + 6p for variable n

Solving:

15 = 3n + 6p

Subtract both sides by 6p

15-6p = 3n +6p -6p\\15-6p=3n

Switch sides of equality

3n=15-6p

Divide both sides by 3

\frac{3n}{3} =\frac{15-6p}{3}\\n=\frac{3(5-2p)}{3}\\n=5-2p

So, solving the equation 15 = 3n + 6p for variable n we get \mathbf{n=5-2p}

8 0
2 years ago
A large nest of recently hatched bald eagles is located at the top of the Eiffel Tower (which is 324 meters tall) and is attract
Mariulka [41]

9514 1404 393

Answer:

  80.5°

Step-by-step explanation:

The applicable trig function is the tangent.

  Tan = Opposite/Adjacent

In this scenario, the side opposite the angle is the tower height, 324 m. The side adjacent is the distance to the tower, 54 m. Then the angle α is related by ...

  tan(α) = 324/54

The value of the angle with this tangent is found using the arctangent function:

  α = arctan(324/54) ≈ 80.5°

She should set her binoculars to 80.5°.

6 0
2 years ago
What is the solution to the system of equations?
krok68 [10]
2x-y=7
y=2x+3
Substitute (2x+3) in for y in the first equation
2x-(2x+3)=7
2x-2x-3=7
-3=7
Becuase -3 does not equal 7 the answer is no solution
4 0
3 years ago
Read 2 more answers
35 hundreds = 5 tens times 7 tens is it true or false
Strike441 [17]
True
if you add an imaginary 0 to the numbers since its in the tenths place you would get 3,500
5(0) x 7(0) = 3,500
3 0
3 years ago
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