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
Given the function defined in the table below, find the average rate of change, in
Usimov [2.4K]

Answer:

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
4/5 divided by 1/3 ??
DochEvi [55]

Answer:

2.4

Step-by-step explanation:

3 0
3 years ago
Henry can write 5 1/4 pages of his novel in 3 hours how may pages does he write per hour
balandron [24]

Answer:

1 3/4

Step-by-step explanation:

5 1/4 / 3 is equal to 1 and 3/4

5 0
3 years ago
Read 2 more answers
the coach for a basketball team wants to buy new shoes for her 12 players. super sport is offering a 20%discount on each pair of
Klio2033 [76]
Here are the calculations for Super Sport:

[12 ($72.50 x 0.8)] 1.065 = $741.24

Here is the math for Double Dribbles:

[12($54.75 x 1.09)] + (12 x $5.99) = $788.01

$788.01 - $741.24 = $46.77

The difference in price is $46.77.

6 0
3 years ago
Find the value of annuity if the periodic deposit is $400 at 4% compounded monthly for 18 years
vlada-n [284]

Answer:

~820.8$

Step-by-step explanation:

The total money (M) after 18 years could be calculated by:

M = principal x (1 + rate)^time

with

principal = 400$

rate = 4% compounded monthly = 0.04/12

time = 18 years = 18 x 12 = 216 months (because of compounded monthly rate)

=> M = 400 x (1 + 0.04/12)^216 = ~820.8$

6 0
3 years ago
Other questions:
  • 115 + ( -215 ) + 315 + ( -415) + 515 + ... + 3915 + ( -4015 ) =
    13·2 answers
  • 4 times the square of one number minus 5 times another number​
    14·1 answer
  • the temperature outside was 50 during the day and fell 16 at night. What was the temperature at night?
    11·2 answers
  • What is the completely simplified equivalent of 2/(5+i)?
    5·1 answer
  • The mass of a penny was measured six times. The following data was reported:
    6·1 answer
  • A polynomial is factored using algebra tiles. What are the factors of the polynomial?
    14·1 answer
  • Find an invertible matrix P and a matrix C of the form such that the matrix A has the form A. The eigenvalues of A are and with
    9·1 answer
  • PLZ HELP ILL MARK BRAINLEST
    10·1 answer
  • Can someone help me plz I will mark brainliest
    6·2 answers
  • Hhhhheeeeeellllllppppp pppppllllllzzzzz!!!!!!!!
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!