Pls do it without guessing

Find the set of solutions for the linear system.

Illusion [34]

Answer:

The system has infinitely many solutions.

$\left\begin{array}{ccc}x_1&=&-\frac{1}{3}x_2-\frac{16}{9}x_4-\frac{2}{9} \\x_2&=&s_1\\x_3&=&-\frac{4}{3}x_4+\frac{1}{3} \\x_4&=&s_2\end{array}\right$

Step-by-step explanation:

To find the solution for this system of linear equations $-3x_1-x_2+4x_3=2\\-3x_3 - 4x_4 = -1$ you must:

Step 1: Transform the augmented matrix to the reduced row echelon form.

A matrix is a rectangular arrangement of numbers into rows and columns.

A system of equations can be represented by an augmented matrix.

In an augmented matrix, each row represents one equation in the system and each column represents a variable or the constant terms.

This is matrix that represents the system

$\left[ \begin{array}{ccccc} -3 & -1 & 4 & 0 & 2 \\\\ 0 & 0 & -3 & 4 & -1 \end{array} \right]$

The augmented matrix can be transformed by a sequence of elementary row operations to the matrix.

There are three kinds of elementary matrix operations.

Interchange two rows (or columns).
Multiply each element in a row (or column) by a non-zero number.
Multiply a row (or column) by a non-zero number and add the result to another row (or column).

Using elementary matrix operations, we get that

Row Operation 1: Multiply the 1st row by -1/3

Row Operation 2: Multiply the 2nd row by -1/3

Row Operation 3: Add 4/3 times the 2nd row to the 1st row

$\left[ \begin{array}{ccccc} 1 & \frac{1}{3} & 0 & \frac{16}{9} & - \frac{2}{9} \\\\ 0 & 0 & 1 & \frac{4}{3} & \frac{1}{3} \end{array} \right]$

Step 2: Interpret the reduced row echelon form

The reduced row echelon form of the augmented matrix is

$\left[ \begin{array}{ccccc} 1 & \frac{1}{3} & 0 & \frac{16}{9} & - \frac{2}{9} \\\\ 0 & 0 & 1 & \frac{4}{3} & \frac{1}{3} \end{array} \right]$

which corresponds to the system

$x_1+\frac{1}{3}x_2+ \frac{16}{9}x_4=-\frac{2}{9} \\x_3+ \frac{4}{3}x_4=\frac{1}{3}$

We see that the variables $x_2, x_4$ can take arbitrary numbers; they are called free variables. Let $x_2=s_1$ , $x_4=s_2$ . All solutions of the system are given by

$\left\begin{array}{ccc}x_1&=&-\frac{1}{3}x_2-\frac{16}{9}x_4-\frac{2}{9} \\x_2&=&s_1\\x_3&=&-\frac{4}{3}x_4+\frac{1}{3} \\x_4&=&s_2\end{array}\right$

The system has infinitely many solutions.

8 0

4 years ago

Quadrilateral ABCD is translated to get quadrilateral A’B’C’D’. Vertex A is at (-5, 2), and vertex A’ is at (2, -2). Quadrilater

Rudik [331]

Answer:

vertex B' is at (1, 1)

Step-by-step explanation:

Let us revise the rules of translation of a point

If the point (x, y) translated horizontally to the right by h units then its image is (x + h, y) ⇒ T (x, y) → (x + h, y)

If the point (x, y) translated horizontally to the left by h units then its image is (x - h, y) ⇒ T (x, y) → (x - h, y)

If the point (x, y) translated vertically up by k units then its image is (x, y + k)→ (x + h, y) ⇒ T (x, y) → (x, y + k)

If the point (x, y) translated vertically down by k units then its image is (x, y - k) ⇒ T (x, y) → (x, y - k)

Let us use the rules to solve our question

∵ Vertex A = (-5, 2)

∵ Vertex A' = (2, -2)

→ The coordinates of the two points changed which means the

quadrilateral is translated horizontally and vertically

∵ The x-coordinate of A = -5

∵ The x-coordinate of A' = 2

→ Which means it moves to the right, so use the first rule above

∴ the rule of translation is T (x, y) → (x + h, y)

∴ x → x + h

∵ x = -5 and x + h = 2

∴ -5 + h = 2

→ Add 5 to both sides

∴ -5 + 5 + h = 2 + 5

∴ h = 7

∴ The quadrilateral is translated 7 units right

∵ The y-coordinate of A = 2

∵ The y-coordinate of A' = -2

→ Which means it moves down, so use the 4th rule above

∴ the rule of translation is T (x, y) → (x, y - k)

∴ y → y - k

∵ y = 2 and y - k = -2

∴ 2 - k = -2

→ Add K to both sides

∴ 2 - k + k = -2 + k

∴ 2 = -2 + k

→ Add 2 to both sides

∴ 2 + 2 = -2 + 2 + k

∴ 4 = k

∴ The quadrilateral is translated 4 units down

→ Let us find B'

∵ T (x, y) → (x + h, y - k) is the rule of translation

∵ B = (-6, 5)

∵ h = 7 and k = 4

∴ B' = (-6 + 7, 5 - 4)

∴ B' = (1, 1)

∴ vertex B' is at (1, 1)

6 0

4 years ago

What does this graph show<br> inverse <br>direct<br> neither

grin007 [14]

Answer:

i think the given graph is inverse

3 0

2 years ago

How much would $300 invested at 7% interest compounded continuously be

Paha777 [63]

The correct awnser would be B because it is the only one rounded to the nearest cent

4 0

3 years ago

Read 2 more answers

What are the mean and the median?

lukranit [14]

Answer: The Mean is 12 while the median is 10.

Step-by-step explanation: To find the mean we need to add all points scored which equals 108 points. Next, you will divide this by the number of players that scored points. Because there are 9 players we will follow 108/9=12. To find the median, you write out each number from smallest to largest or largest to smallest and find the number in the middle, this should act somewhat like an average however i would recommend using the mean to find an average. When writing out all the number they should look something like this: 6,7,7,7,10,11,13,23,24

Now that we have written them out, we find the middle most number which is 10 which means that our median is 10.

The mean is 12 points.

The median is 10 points.

7 0

3 years ago