1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
spayn [35]
3 years ago
12

Use matrices and elementary row to solve the following system:

Mathematics
1 answer:
LiRa [457]3 years ago
5 0

I assume the first equation is supposed to be

5x-3y+2z=13

and not

5x-3x+2x=4x=13

As an augmented matrix, this system is given by

\left[\begin{array}{ccc|c}5&-3&2&13\\2&-1&-3&1\\4&-2&4&12\end{array}\right]

Multiply through row 3 by 1/2:

\left[\begin{array}{ccc|c}5&-3&2&13\\2&-1&-3&1\\2&-1&2&6\end{array}\right]

Add -1(row 2) to row 3:

\left[\begin{array}{ccc|c}5&-3&2&13\\2&-1&-3&1\\0&0&5&5\end{array}\right]

Multiply through row 3 by 1/5:

\left[\begin{array}{ccc|c}5&-3&2&13\\2&-1&-3&1\\0&0&1&1\end{array}\right]

Add -2(row 3) to row 1, and add 3(row 3) to row 2:

\left[\begin{array}{ccc|c}5&-3&0&11\\2&-1&0&4\\0&0&1&1\end{array}\right]

Add -3(row 2) to row 1:

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

Multiply through row 1 by -1:

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

Add -2(row 1) to row 2:

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

Multipy through row 2 by -1:

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

The solution to the system is then

\boxed{x=1,y=-2,z=1}

You might be interested in
WILL MARK BRAINLIEST <br><br> what is the domain of (f/g) (x)?
tatyana61 [14]

Given that f(x) = \sqrt{7-x} and g(x) = \sqrt{x + 2}, we can say the following:

\Bigg(\dfrac{f}{g}\Bigg)(x) = \dfrac{f (x)}{g(x)} = \dfrac{\sqrt{7 - x}}{\sqrt{x+2}}


Now, remember what happens if we have a negative square root: it becomes an imaginary number. We don't want this, so we want to make sure whatever is under a square root is greater than 0 (given we are talking about real numbers only).


Thus, let's set what is under both square roots to be greater than 0:

\sqrt{7 - x} \Rightarrow 7 - x \geq 0 \Rightarrow x \leq 7

\sqrt{x + 2} \Rightarrow x + 2 \geq 0 \Rightarrow x \geq -2


Since both of the square roots are in the same function, we want to take the union of the domains of the individual square roots to find the domain of the overall function.

x \leq 7 \,\,\cup x \geq -2 = \boxed{-2 \leq x \leq 7}


Now, let's look back at the function entirely, which is:

\Bigg( \dfrac{f}{g} \Bigg)(x) = \dfrac{\sqrt{7 - x}}{\sqrt{x+2}}

Since \sqrt{x + 2} is on the bottom of the fraction, we must say that \sqrt{x + 2} \neq 0, since the denominator can't equal 0. Thus, we must exclude \sqrt{x + 2} = 0 \Rightarrow x + 2 = 0 \Rightarrow x = -2 from the domain.


Thus, our answer is Choice C, or \boxed{ \{ x | -2 < x \leq 7 \}}.


<em>If you are wondering why the choices begin with the x | symbol, it is because this is a way of representing that x lies within a particular set.</em>

6 0
3 years ago
Express 0.125 as a fraction in its lowest form.
guapka [62]
1/8 is your answer
-Hope this helps
5 0
3 years ago
Read 2 more answers
Is there any way to post images on your questions?
AysviL [449]

yeah there is u should be able to by clicking on the paper clip                                          


7 0
3 years ago
Tickets to the school musical are $5.00 for adults and $3.50 for students. If the total value of the tickets sold was $2517.50 a
stealth61 [152]
To answer this, you will write and equation in terms of the number of adult tickets sold and then solve for a, the number of adult tickets.

$5a + $3.50s = $2517.50
$5a + $3.50(a + 100) = $2517.50
5a + 3.50a + 350 = 2517.50
         8.50a  -350      -350
                  <u>8.5a</u>  = <u>2167.50</u>
                  8.5         8.5
    a = 255
The number of adult tickets sold was 255, and the number of student tickets sold was 355 (255 +100).


7 0
3 years ago
Here's the question ​
zheka24 [161]

Answer:

60

Step-by-step explanation:

perimeter (p) = 8 + 17 + 15 = 40

semi-perimeter (s) = p/2 = 20

Area = square root of s(s-a)(s-b)(s-c) where a,b,c are the sides of the triange by Herons formula.

Therefore, area = 20(20-8)(20-15)(20-17) = square root of 3600 = 60

4 0
3 years ago
Other questions:
  • Please help me solve this problem for my homework .<br> X= ?<br><br> 9<br> 16<br> 4
    11·1 answer
  • Create a trinomial that can be factored and write it in standard form.
    9·1 answer
  • 2x - 7y = 2 and 3x + y = -20 addition/elimination
    10·1 answer
  • Many drove 45 miles in 0.75 hours. What was the average rate he drove in miles per hour
    13·2 answers
  • Is 5/3 a terminal or repeating decimal
    8·2 answers
  • Milagro needs to find an expression that represents the shaded area below. Which expression is equivalent to the area of the sha
    15·1 answer
  • Can someone solve this and show it step by step<br><br> −5x + 2[x − (4 + 2x)] ≥ 5 − 2(x − 1)
    7·2 answers
  • Domain, range, etc. please help
    6·1 answer
  • Please help me on this
    11·1 answer
  • There are tulips, daisies, and daffodils growing in a garden. There are 2 times as
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!