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
Musya8 [376]
3 years ago
7

Use the augmented matrix method to solve the following system of equations. Your answers may be given as decimals or fractions.

Mathematics
1 answer:
Alexandra [31]3 years ago
7 0

Answer:

x\ =\ \dfrac{21}{5}

y\ =\ \dfrac{3}{5}

z = 2

Step-by-step explanation:

Given equations are

x - 2y - z = 2

x + 3y - 2z = 4

-x + 2y + 3z = 2

from the given equations the augmented matrix can be written as

\left[\begin{array}{ccc}1&-2&-1:2\\1&3&-2:4\\-1&2&3:2\end{array}\right]

R_2=>R_2-R_1\ and\ R_3=>R_3+R_1

=\ \left[\begin{array}{ccc}1&-2&-1:2\\0&5&-1:2\\0&0&2:4\end{array}\right]

R_2=>\dfrac{R_2}{5}

=\ \left[\begin{array}{ccc}1&-2&-1:2\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\0&0&2:4\end{array}\right]

R_1=>R_1+2.R_2

=\ \left[\begin{array}{ccc}1&0&-1-\dfrac{2}{5}:2+\dfrac{4}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&2:4\end{array}\right]

=\ \left[\begin{array}{ccc}1&0&\dfrac{-7}{5}:\dfrac{14}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&2:4\end{array}\right]

R_3=>\dfrac{R_3}{2}

=\ \left[\begin{array}{ccc}1&0&\dfrac{-7}{5}:\dfrac{14}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&1:2\end{array}\right]

R_1=>R_1+\dfrac{7}{5}R_3\ and\ R_2+\dfrac{1}{5}R_3

=\ \left[\begin{array}{ccc}1&0&0:\dfrac{14}{5}+\dfrac{7}{5}\\\\0&1&0:\dfrac{2}{5}+\dfrac{1}{5}\\\\0&0&1:2\end{array}\right]

So, from the above augmented matrix, we can write

x\ =\ \dfrac{21}{5}

y\ =\ \dfrac{3}{5}

z = 2

You might be interested in
Sum and difference of 5+2.3
professor190 [17]

Answer:

sum: 7.3 difference:2.7

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
What is the first step to verify that the following identity is true?
umka2103 [35]

Step-by-step explanation:

this right ans according to your question

8 0
3 years ago
Which of the following ordered pairs is a solution of the line y-2x=6
Novay_Z [31]

<u><em>Answer:</em></u>

<u><em>x = -3 + Y/2</em></u>

<u><em>y= 6 +  2x</em></u>

<u><em>Hope this helps!:3</em></u>

7 0
3 years ago
Read the following bar graph and answer the following related questions :
Varvara68 [4.7K]
  1. apala
  2. meenu
  3. 1:2
  4. 4 girls..

3 0
3 years ago
Read 2 more answers
What’s the value of x?
tatuchka [14]
We have a pair of vertical angles here. So they would equal each other.
3x+50=6x-10
Subtract 3x to 6x:
50=3x-10
Add 10 to 50:
60=3x
Divide 3 to both sides:
x=30
4 0
3 years ago
Read 2 more answers
Other questions:
  • Find the surface area of each triangular prism
    8·1 answer
  • How much would a sales discount be on an invoice that totals 3,000, is dated January 14th, has terms of 2/10bnet30, and is paid
    5·1 answer
  • PQRS is a quadrilateral. &lt;PQR = (7x-2) PSR = (5x+14) what is the measure of angles PQR and PSR?
    15·1 answer
  • In how many different ways can you answer a multiple choice test that has 5 questions and 3 choices for each answer?
    6·1 answer
  • Consider the 1-to10^19 scale on which the disk of the Milky Way Galaxy fits on a football field. On this scale, how far is it fr
    7·2 answers
  • Plzzzzzz helppppp asappppp <br> ****will mark brainliest ****
    6·1 answer
  • The area of a triangle is 1,440 cm2. The base of the triangle is 5 times the height. What is the height of the triangle?
    7·2 answers
  • 1.0*10^-11 + 1.0 x 10^-8
    6·1 answer
  • Barry collects comic books. He currently has 350 comic books and plans to buy 10 comic books each month. Which equation represen
    12·1 answer
  • Help please!!!!!!!!!
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!