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bazaltina [42]
3 years ago
10

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

3z=-2. 6x+2y+2z=-48. x+4y+3z=-38​
Mathematics
1 answer:
Alekssandra [29.7K]3 years ago
7 0

Answer:

x = -5, y = -6, z = -3

Step-by-step explanation:

Given the system of three equations:

\left\{\begin{array}{l}x-2y+3z=-2\\6x+2y+2z=-48\\x+4y+3z=-38\end{array}\right.

Write the augmented matrix for the system of equations

\left(\begin{array}{ccccc}1&-2&3&|&-2\\6&2&2&|&-48\\1&4&3&|&-38\end{array}\right)

Find the reduced row-echelon form of the augmented matrix for the system of equations:

\left(\begin{array}{ccccc}1&-2&3&|&-2\\6&2&2&|&-48\\1&4&3&|&-38\end{array}\right)\sim \left(\begin{array}{ccccc}1&-2&3&|&-2\\0&-14&16&|&36\\0&-6&0&|&36\end{array}\right)\sim \left(\begin{array}{ccccc}1&3&-2&|&-2\\0&16&-14&|&36\\0&0&-6&|&36\end{array}\right)

Thus, the system of three equations is

\left\{\begin{array}{r}x+3z-2y=-2\\16z-14y=36\\-6y=36\end{array}\right.

From the last equation:

y=-6

Substitute it into the second equation:

16z-14\cdot (-6)=36\\ \\16z=36-84\\ \\16z=-48\\ \\z=-3

Substitute y = -6 and z = -3 into the first equation:

x+3\cdot (-3)-2\cdot (-6)=-2\\ \\x=-2+9-12\\ \\x=-5

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Then, we calculate for the summation of the squares of differences of these numbers from the mean, S
 
                             S  = (1 - 3)² + (2 - 3)² + (3 - 3)² + (4 - 3)² + (5 - 3)²
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Divide this summation by the number of items and take the square root of the result to get the standard deviation.

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Does the value of x make the equation to 0. Why?
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Since there is no value of x that will ever make this a true statement, the solution to the equation above is “no solution”. Be careful that you do not confuse the solution x = 0 with “no solution”. The solution x = 0 means that the value 0 satisfies the equation, so there is a solution.

Step-by-step explanation:

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The pattern is formed a geometric sequence

The nth term of the sequence is a_{n}=3^{n}

Step-by-step explanation:

The formula of the nth term of a geometric sequence is:

a_{n}=ar^{n-1} , where

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∵ The pattern is 3 , 9 , 27 , 81 , 243

∵ 9 ÷ 3 = 3

∵ 27 ÷ 9 = 3

∵ 81 ÷ 27 = 3

∵ 243 ÷ 81 = 3

- There is a common ratio 3 between each two consecutive terms

∴ The pattern is formed a geometric sequence

∵ The first term is 3

∴ a = 3

∵ The common ratio is 3

∴ r = 3

- To find the nth term substitute a and r in the formula above

∵ a_{n}=ar^{n-1}

∴ a_{n}=3(3)^{n-1}

- Remember we add the powers of the same base with multiplication

∵ 3 × 3^{n-1} = 3^{1+n-1}

∴ 3 × 3^{n-1} = 3^{n}

∴ a_{n}=3^{n}

∴ The nth term of the sequence is  a_{n}=3^{n}

Learn more:

You can learn more about the sequences in brainly.com/question/1522572

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In a class of P students, the average of test scores is 70. In another class the average test scores is 92. When scores of the t
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So, since averages are defined as:

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So, using that logic, the other class can be represented as:

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We can take both of these equations and multiply them by N:

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So, if we want to find the average of this we should add both our equations then divide by P+N, which is the number of all the students.

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Simplified we would have P/N=3/8.

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