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
Lana71 [14]
3 years ago
5

Find all solutions by transforming the system to reduced echelon form and back substituting. (If there are an infinite number of

solutions use s1 as your parameter. If there is no solution, enter NO SOLUTION.)
2x1 + x2 = 2

−x1 − x2 − x3 = 4
Mathematics
1 answer:
Zolol [24]3 years ago
3 0

Answer:

The system has infinite solutions described in the set \{(x_1,x_2,x_3)=(6+s1, -10-2s1,s1): s1\in\mathbb{R}\}

Step-by-step explanation:

The augmented matrix of the system is \left[\begin{array}{cccc}-1&-1&-1&4\\2&1&0&2\end{array}\right].

We apply row operations:

1. We add the first row to the second row twice and obtain the matrix \left[\begin{array}{cccc}-1&-1&-1&4\\0&-1&-2&10\end{array}\right]

2. multiply by -1 the rows of the previous matrix and obtain the matrix \left[\begin{array}{cccc}1&1&1&-4\\0&1&2&-10\end{array}\right] that is the reduced echelon form of the matrix associated to the system.

Now we aply backward substitution:

1. Observe that the reduced echelon form has a free variable, then the system has infinite solutions.

2.

x_2+2x_3=-10\\x_2=-10-2x_3

3.

x_1+x_2+x_3=-4\\x_1-10-2x_3+x_3=-4\\x_1-x_3=-4+10\\x_1=6+x_3.

Then the set of solutions is \{(x_1,x_2,x_3)=(6+s1, -10-2s1,s1): s1\in\mathbb{R}\}

You might be interested in
Pls solve this with step by step.
MAVERICK [17]

Step-by-step explanation:

-x+5+6x-7x-14

6x-8x+5-14

-2x-9

3 0
1 year ago
Nine increased by the product of a number and 2 is less than or equal to 27.
Naily [24]

Answer:

x≤9

Step-by-step explanation:

9+2x≤27

1) Subtract both sides by 9:

2x≤18

2) Divide both sides by 2:

x≤9

8 0
3 years ago
Pyramids and cones have how many base
Blababa [14]

Answer:

pyramids and cones have 1 base.

Step-by-step explanation:

4 0
2 years ago
-6(x-3)<br><br><br><br><br><br><br><br><br><br><br> pls help me....
MariettaO [177]

Answer:

−6x+18

Step-by-step explanation:

-6(x-3)

(−6)(x+−3)

=(−6)(x)+(−6)(−3)

=−6x+18

4 0
3 years ago
Read 2 more answers
There is a closed carton of eggs in Mai's refrigerator. The carton contains e eggs and it can hold 12 eggs. What does the inequa
den301095 [7]

Answer:

That the number of eggs (e) in the carton is less than 12

Step-by-step explanation:

7 0
2 years ago
Other questions:
  • What is x^2-2x-3=0 and in the simplest radical form
    7·2 answers
  • PLEASE HELP ME ASAP!!! ILL MARK BRIANLIEST AND GIVE EXTRA POINTS1. When writing a linear equation for a word problem, what are s
    15·1 answer
  • List the next four multiples of the fraction 3/5
    14·2 answers
  • Over a period of 12 hours the temperature dropped 36 degrees Fahrenheit. What was the average change in temperature in one hour
    11·1 answer
  • find the slope and y-intercept for a line passing through the following two points,then create a slope intercept equation (-2,2)
    9·1 answer
  • What are the x-values of the quadratic equation (x-2)^2-9=0?
    6·1 answer
  • -1/3 + 5e = -3/4 <br> Pls show your work
    13·1 answer
  • Please help ASAP. Will give brainliest!
    5·1 answer
  • No links and no wrong answer please help i'll mark you the brainlest.
    10·1 answer
  • Rania receives $40 for her birthday. Then he spends $15 at the movies.
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!