please help!!
Write a matrix representing the system of equations

Answer:

[tex](4, -1, 3)[/tex]

Step-by-step explanation:

We have the system of equations:

[tex]\left\{ \begin{array}{ll} x+2y+z =5 \\ 2x-y+2z=15\\3x+y-z=8 \end{array} \right.[/tex]

We can convert this to a matrix. In order to convert a triple system of equations to matrix, we can use the following format:

[tex]\begin{bmatrix}x_1& y_1& z_1&c_1\\x_2 & y_2 & z_2&c_2\\x_3&y_2&z_3&c_3 \end{bmatrix}[/tex]

Importantly, make sure the coefficients of each variable align vertically, and that each equation aligns horizontally.

In order to solve this matrix and the system, we will have to convert this to the reduced row-echelon form, namely:

[tex]\begin{bmatrix}1 & 0& 0&x\\0 & 1 & 0&y\\0&0&1&z \end{bmatrix}[/tex]

Where the (x, y, z) is our solution set.

Reducing:

With our system, we will have the following matrix:

[tex]\begin{bmatrix}1 & 2& 1&5\\2 & -1 & 2&15\\3&1&-1&8 \end{bmatrix}[/tex]

What we should begin by doing is too see how we can change each row to the reduced-form.

Notice that R₁ and R₂ are rather similar. In fact, we can cancel out the 1s in R₂. To do so, we can add R₂ to -2(R₁). This gives us:

[tex]\begin{bmatrix}1 & 2& 1&5\\2+(-2) & -1+(-4) & 2+(-2)&15+(-10) \\3&1&-1&8 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\0 & -5 & 0&5 \\3&1&-1&8 \end{bmatrix}[/tex]

Now, we can multiply R₂ by -1/5. This yields:

[tex]\begin{bmatrix}1 & 2& 1&5\\ -\frac{1}{5}(0) & -\frac{1}{5}(-5) & -\frac{1}{5}(0)& -\frac{1}{5}(5) \\3&1&-1&8 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\3&1&-1&8 \end{bmatrix}[/tex]

From here, we can eliminate the 3 in R₃ by adding it to -3(R₁). This yields:

[tex]\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\3+(-3)&1+(-6)&-1+(-3)&8+(-15) \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0&-5&-4&-7 \end{bmatrix}[/tex]

We can eliminate the -5 in R₃ by adding 5(R₂). This yields:

[tex]\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0+(0)&-5+(5)&-4+(0)&-7+(-5) \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0&0&-4&-12 \end{bmatrix}[/tex]

We can now reduce R₃ by multiply it by -1/4:

[tex]\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\ -\frac{1}{4}(0)&-\frac{1}{4}(0)&-\frac{1}{4}(-4)&-\frac{1}{4}(-12) \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}[/tex]

Finally, we just have to reduce R₁. Let's eliminate the 2 first. We can do that by adding -2(R₂). So:

[tex]\begin{bmatrix}1+(0) & 2+(-2)& 1+(0)&5+(-(-2))\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 0& 1&7\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}[/tex]

And finally, we can eliminate the second 1 by adding -(R₃):

[tex]\begin{bmatrix}1 +(0)& 0+(0)& 1+(-1)&7+(-3)\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 0& 0&4\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}[/tex]

Therefore, our solution set is [tex](4, -1, 3)[/tex]

And we're done!

3. Which ratio is not equivalent to 5 : 8?
A. 10 out of 18
B. 15 to 24
20
C.
32
D. 10:16

Easy question for easy points.

Solve for the unknown value
X/0.45=0.16/1.2

Give an example of each of the following, or argue that such a request is impossible.

a. A sequence that has a subsequence that is bounded but contains no subsequence that converges.
b. A sequence that does not contain 0 or 1 as a term but contains subsequences converging to each of these values.
c. A sequence that contains subsequences converging to every point in the infinite set {1, 1/2, 1/3, 1/4, 1/5,...}.
d. A sequence that contains subsequences converging to every point in the infinite set {1, 1/2, 1/3, 1/4, 1/5,...}, and no subsequences converging to points outside of this set.

Escribe un número decimal que se encuentre entre cada Par de números 0.1 y 0.01?

simplify (1-2i) + (-2-i)

2 cities are 120 miles apart. A group that is travelling from one of the cities to the other is already 3/4 of the way. How many miles do the group have left to travel?
Answer in this from, They have blank miles to go

10,000 is a what of 10 because 10 x 10 x 10= 10,000

Ali graphs the function f(x) = –(x + 2)2 – 1 as shown. On a coordinate plane, a parabola opens up. It goes through (negative 3, 0), has a vertex at (negative 2, negative 1), and goes through (negative 1, 0). A vertical dashed line at (negative 2, 0) is parallel to the y-axis. Which best describes the error in the graph?

how do I multiply (3.4)(6.7) explain your answers and how you got that please. ​

What’s 11673.15175 nearest cent

Sarah went on a 36 mile trip to a soccer game. On the way back, due to road construction she had to drive 18 miles per hour slower. This made the trip take 1 hour longer. How fast did she drive to the soccer game?

Help me please its urgent I need it done asap I need help if anyone could help me solve these problems that would be very helpful! (I'll give brainliest if you can solve all of them!) A company designs a circular dartboard such that the target area in the center is surrounded by a safety margin. Federal law requires that the area of the safety margin must be twice the area of the actual target in the center. If the total radius of the dartboard is 3 feet, what is the radius of the circular target in the center? (you must show the algebra for full credit)

If g(x) = x2 + 2, find g(3).
9
8
11
6

Given f(x) and g(x) = f(x + k), use the graph to determine the value of k.

Two lines labeled f of x and g of x. Line f of x passes through points 0, 4 and negative 4, 0. Line g of x passes through points negative 9, 0 and negative 4, 5.

−4
−5
4
5

3 lines are shown. A line with points A, F, D intersects a line with points B, F, E at point F. A line extends from point F to point C in between angle B F D.
Which angle is a vertical angle with AngleEFD?

AngleDFB
AngleCED
AngleBFC
AngleAFB

3 times as many footballs as voleyballs were sold

If you walk 5 miles in 50 minutes, then you will walk how far in 90 minutes if you walk at the same speed the whole time? If necessary, round your answer to the nearest tenth of a mile.

If $5000 was invested at a rate of 5%, how many years would it take to triple if it is compounded daily

determine the type of triangle that is drawn below.

scalene right
scalene obtuse
isosceles right
scalene acute
isosceles obtuse
equilateral
isosceles acute

A rectangular city is 2 miles long and 7 miles wide. What is the distance between opposite corners of the city? The exact distance is ______________ miles How far is it to the closest tenth of a mile? Answer: The distance is approximately ___________ miles.

help me pls ☹️☹️☹️☹️​

The model represents an equation. What value of x makes the equation true?
A) -15
B) -3
C) 15
D) 3​

pleas yall help me with this cause I'm dumb

Given ABCD: EFGH, what is the measure of H?
A. 70°
B. 74
C. 100
D. 116

Please help. Will give brainliest

PLEASE ANSWER ASAP


the picture is below btw 0_0

what is 4 times x and pls explain it for me so then I can explain it​

Emilio's Bakery is getting more and more orders for blackberry pies. The bakers made 16 blackberry pies in December, 48 blackberry pies in January, 144 blackberry pies in February, and 432 blackberry pies in March. What kind of sequence is this? arithmetic or geometric

Marsha wants to put a wallpaper border around her bedroom. How much border will she need if her room is 13 ¾ feet long by 12 ½ feet wide