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Viktor [21]
3 years ago
15

Darren multiplied 0 x 1 x 1 = 1 is his answer correct

Mathematics
1 answer:
Gnoma [55]3 years ago
5 0
No his answer is not correct, anything times 0 is always going to be 0. So it is impossible that his answer would be 1.
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Solve the system of linear equations using the Gauss-Jordan elimination method. 2x + 3y 6212 3x + (x, y. z)
Gekata [30.6K]

Answer:

The solution of the system of linear equations is x=3, y=4, z=1

Step-by-step explanation:

We have the system of linear equations:

2x+3y-6z=12\\x-2y+3z=-2\\3x+y=13

Gauss-Jordan elimination method is the process of performing row operations to transform any matrix into reduced row-echelon form.

The first step is to transform the system of linear equations into the matrix form. A system of linear equations can be represented in matrix form (Ax=b) using a coefficient matrix (A), a variable matrix (x), and a constant matrix(b).

From the system of linear equations that we have, the coefficient matrix is

\left[\begin{array}{ccc}2&3&-6\\1&-2&3\\3&1&0\end{array}\right]

the variable matrix is

\left[\begin{array}{c}x&y&z\end{array}\right]

and the constant matrix is

\left[\begin{array}{c}12&-2&13\end{array}\right]

We also need the augmented matrix, this matrix is the result of joining the columns of the coefficient matrix and the constant matrix divided by a vertical bar, so

\left[\begin{array}{ccc|c}2&3&-6&12\\1&-2&3&-2\\3&1&0&13\end{array}\right]

To transform the augmented matrix to reduced row-echelon form we need to follow these row operations:

  • multiply the 1st row by 1/2

\left[\begin{array}{ccc|c}1&3/2&-3&6\\1&-2&3&-2\\3&1&0&13\end{array}\right]

  • add -1 times the 1st row to the 2nd row

\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&-7/2&6&-8\\3&1&0&13\end{array}\right]

  • add -3 times the 1st row to the 3rd row

\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&-7/2&6&-8\\0&-7/2&9&-5\end{array}\right]

  • multiply the 2nd row by -2/7

\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&-7/2&9&-5\end{array}\right]

  • add 7/2 times the 2nd row to the 3rd row

\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&0&3&3\end{array}\right]

  • multiply the 3rd row by 1/3

\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&0&1&1\end{array}\right]

  • add 12/7 times the 3rd row to the 2nd row

\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&0&4\\0&0&1&1\end{array}\right]

  • add 3 times the 3rd row to the 1st row

\left[\begin{array}{ccc|c}1&3/2&0&9\\0&1&0&4\\0&0&1&1\end{array}\right]

  • add -3/2 times the 2nd row to the 1st row

\left[\begin{array}{ccc|c}1&0&0&3\\0&1&0&4\\0&0&1&1\end{array}\right]

From the reduced row echelon form we have that

x=3\\y=4\\z=1

Since every column in the coefficient part of the matrix has a leading entry that means our system has a unique solution.

7 0
3 years ago
Find the distance between the points (7, –5) and (–2, –4).
nasty-shy [4]

9.055

Step-by-step explanation:

distance

= √(x₁ - x₂)² + (y₁ - y₂)

= √[7 - (-2)]² + [-5 - (-4)]²

= √[9]² + [-1]²

= √(81 + 1)

= √82

≈ 9.055

3 0
3 years ago
The sum of two numbers is 18 and their difference is 8
Volgvan

Answer:

13 and 5

Step-by-step explanation:

x+y=18

x-y=8

_____

2x=26

x=13

So the first number must be 13

13+y=18

y=5

And the second number must be 5

8 0
3 years ago
Read 2 more answers
I need the measurement of each angle (please show work)
aliya0001 [1]

Answer:

∠E = ∠F = 41°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 given angles and equate to 180

x + x + 98 = 180 ( subtract 98 from both sides )

2x = 82 ( divide both sides by 2 )

x = 41

Hence

∠E = ∠F = 41°

3 0
3 years ago
What is the total measure of an average man's brain and heart in kilograms
mel-nik [20]
3 by 10kg?          ioooooooooooooo    
4 0
3 years ago
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