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
azamat
1 year ago
6

Solve the system of equations using matrices. Use the Gauss- Jordan elimination method And find a solution set

Mathematics
1 answer:
KATRIN_1 [288]1 year ago
6 0
\begin{gathered} x+y+z=4 \\ x-y-z=0 \\ x-y+z=8 \\ \text{The system using matrix is} \\ \begin{bmatrix}{1} & {1} & {1}, & {4} \\ {1} & {-1} & {-1,} & {0} \\ {1} & {-1} & {1,} & {8}{}{}\end{bmatrix}\rightarrow F2=F2-F1=\begin{bmatrix}{1} & {1} & {1}, & {4} \\ {0} & {-2} & {-2,} & {-4} \\ {1} & {-1} & {1,} & {8}{}{}\end{bmatrix} \\ \rightarrow F3=F3-F1=\begin{bmatrix}{1} & {1} & {1}, & {4} \\ {0} & {-2} & {-2,} & {-4} \\ {0} & {-2} & {0,} & {4}{}{}\end{bmatrix}\rightarrow F2=-\frac{1}{2}F2 \\ =\begin{bmatrix}{1} & {1} & {1}, & {4} \\ {0} & {1} & {1,} & {2} \\ {0} & {-2} & {0,} & {4}{}{}\end{bmatrix}\rightarrow F3=F3+2F2=\begin{bmatrix}{1} & {1} & {1}, & {4} \\ {0} & {1} & {1,} & {2} \\ {0} & {0} & {2,} & {8}{}{}\end{bmatrix}\rightarrow F3=\frac{1}{2}F3 \\ =\begin{bmatrix}{1} & {1} & {1}, & {4} \\ {0} & {1} & {1,} & {2} \\ {0} & {0} & {1,} & {4}{}{}\end{bmatrix}\rightarrow F2=F2-F3=\begin{bmatrix}{1} & {1} & {1}, & {4} \\ {0} & {1} & {0,} & {-2} \\ {0} & {0} & {1,} & {4}{}{}\end{bmatrix} \\ \rightarrow F1=F1-F3=\begin{bmatrix}{1} & {1} & {0}, & {0} \\ {0} & {1} & {0,} & {-2} \\ {0} & {0} & {1,} & {4}{}{}\end{bmatrix}\rightarrow F1=F1-F2 \\ =\begin{bmatrix}{1} & {0} & {0}, & {2} \\ {0} & {1} & {0,} & {-2} \\ {0} & {0} & {1,} & {4}{}{}\end{bmatrix} \\ \text{Therefore, the solution is }x=2,\text{ y=-2 and z=4} \end{gathered}

You might be interested in
The radius of circle O is 24 and OC = 13. Find AB.
irinina [24]

Answer:

what does oc mean?

Step-by-step explanation:

7 0
3 years ago
Which expression is equivalent to the following complex fraction?
True [87]

Answer:

<h2>A. -2y+5x/3x-2y</h2>

Step-by-step explanation:

Given the complex fraction;

-\frac{2}{x} +\frac{5}{y} / \frac{3}{y} - \frac{2}{x} \\

First we will find the LCM of the numerator and the denominator as shown below;

\frac{-2y+5x}{xy} /\frac{3x-2y}{xy}

Then we divide both equation by multiplying the numerator by the reciprocal of the denominator as shown;

= \frac{-2y+5x}{xy} * \frac{xy}{3x-2y}  \\= \frac{-2y+5x}{3x-2y} \\

This gives the required answer

5 0
3 years ago
Most of the People in the middle east are Muslim and speak Arabic. Which of the following does this explain?
Alenkinab [10]

a is the answerStep-by-step explanation:

3 0
3 years ago
Read 2 more answers
The cash price of a bike is $3000. The bike can be bought on hire purchase by making a 25% down-payment and monthly payments of
horrorfan [7]
25% downpayment of $750 + $125 x 24 months

= $3750
8 0
3 years ago
Read 2 more answers
Is 19 a prime number or composite?
Alexandra [31]
Prime, because the only number that can go into it are 19 and 1
5 0
3 years ago
Read 2 more answers
Other questions:
  • Eli needs pieces of ribbon cut into strips that are 2 1/2 feet long. The roll of ribbon is 7 1/2 feet long. Which expression cou
    8·1 answer
  • For math Equations what is 4x + 5 = x + 8??
    7·2 answers
  • Miranda bought some apples and oranges at the store for fruit salad. Owen bought three times as many apples and twice as many or
    9·2 answers
  • Point D is on AC If M
    14·1 answer
  • You deposit $50 in a bank that offers 6% yearly compound interest and you add another $50 at the beginning of each year for anot
    11·1 answer
  • Most people think babies are equally likely to come as either a boy or a girl. This is not true. Actually, about 51.3% of all ba
    5·1 answer
  • In need of help, PLEASEEEE AND THANK YOUUUUUUUUUU &lt;3
    5·1 answer
  • A b and c are different questions
    9·2 answers
  • You sell instruments at a Caribbean music festival. You earn $326 by selling 12 sets of maracas, 6 sets of ​claves, and x djembe
    6·2 answers
  • (iv) In the figure, there are(a) one ray and an intersecting point (b) two rays and an intersecting point(c) one ray and two int
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!