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
Free_Kalibri [48]
3 years ago
7

Find the set of solutions for the linear system.

Mathematics
1 answer:
Illusion [34]3 years ago
8 0

Answer:

The system has infinitely many solutions.

\left\begin{array}{ccc}x_1&=&-\frac{1}{3}x_2-\frac{16}{9}x_4-\frac{2}{9}  \\x_2&=&s_1\\x_3&=&-\frac{4}{3}x_4+\frac{1}{3}  \\x_4&=&s_2\end{array}\right

Step-by-step explanation:

To find the solution for this system of linear equations -3x_1-x_2+4x_3=2\\-3x_3 - 4x_4 = -1you must:

Step 1: Transform the augmented matrix to the reduced row echelon form.

A matrix is a rectangular arrangement of numbers into rows and columns.

A system of equations can be represented by an augmented matrix.

In an augmented matrix, each row represents one equation in the system and each column represents a variable or the constant terms.

This is matrix that represents the system

\left[ \begin{array}{ccccc} -3 & -1 & 4 & 0 & 2 \\\\ 0 & 0 & -3 & 4 & -1 \end{array} \right]

The augmented matrix can be transformed by a sequence of elementary row operations to the matrix.

There are three kinds of elementary matrix operations.

  1. Interchange two rows (or columns).
  2. Multiply each element in a row (or column) by a non-zero number.
  3. Multiply a row (or column) by a non-zero number and add the result to another row (or column).

Using elementary matrix operations, we get that

Row Operation 1: Multiply the 1st row by -1/3

Row Operation 2: Multiply the 2nd row by -1/3

Row Operation 3: Add 4/3 times the 2nd row to the 1st row

\left[ \begin{array}{ccccc} 1 & \frac{1}{3} & 0 & \frac{16}{9} & - \frac{2}{9} \\\\ 0 & 0 & 1 & \frac{4}{3} & \frac{1}{3} \end{array} \right]

Step 2: Interpret the reduced row echelon form

The reduced row echelon form of the augmented matrix is

\left[ \begin{array}{ccccc} 1 & \frac{1}{3} & 0 & \frac{16}{9} & - \frac{2}{9} \\\\ 0 & 0 & 1 & \frac{4}{3} & \frac{1}{3} \end{array} \right]

which corresponds to the system

x_1+\frac{1}{3}x_2+ \frac{16}{9}x_4=-\frac{2}{9} \\x_3+ \frac{4}{3}x_4=\frac{1}{3}

We see that the variables x_2, x_4 can take arbitrary numbers; they are called free variables. Let x_2=s_1, x_4=s_2. All solutions of the system are given by

\left\begin{array}{ccc}x_1&=&-\frac{1}{3}x_2-\frac{16}{9}x_4-\frac{2}{9}  \\x_2&=&s_1\\x_3&=&-\frac{4}{3}x_4+\frac{1}{3}  \\x_4&=&s_2\end{array}\right

The system has infinitely many solutions.

You might be interested in
Which amount is largest? 1kg 1dg 100g 1000mg
Paul [167]

Answer:

your answer would be 1kg

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Given rectangle ABCD with vertices A(1, 4), B(3, 6), C(6, 3), and D(4, 1), what is the
Hitman42 [59]

Answer:

  10√2

Step-by-step explanation:

A(1, 4), B(3, 6), C(6, 3), D(4, 1)

The distance formula tells you the distance d between two points (x1, y1) and (x2, y2) is given by ...

  d = √((x2-x1)² +(y2-y1)²

Then the side lengths are ...

  AB = √(2² +2²) = √8 = 2√2

  BC = √(3² +(-3)²) = √18 = 3√2

The perimeter is twice the sum of these sides, so is ...

  P = 2(2√2 +3√2) = 10√2 . . . the perimeter of the rectangle

6 0
3 years ago
What is 65 miles in 2.7 gallons unit rate rounded to the nearest hundredth
STALIN [3.7K]
You can't convert miles into gallons those are two different units of measurement.
4 0
3 years ago
Read 2 more answers
the seventh grade class is putting on a variety show to raise money. it cost 700 dollars to rent the banquet hall that they are
nexus9112 [7]

Answer:

Since the question is partial, i will assume 2 scenarios:

They need to raise 1000 income

They need to make 1000 as profit

If $1000 as income:

Each ticket costs $15, so  tickets would bring them $1000 income. Fractional ticket is not possible, so rounding gives us 67 tickets as the answer.

If $1000 as profit:

Their cost of renting is $700. We know that .

So, . So, to raise $1700, we need  tickets. Fractional ticket is not possible, so rounding gives us 114 tickets as the answer.

ANSWER:

If need to raise atleast $1000 as income, they need to sell 67 tickets.

If need to raise atleast $1000 as profit, they need to sell 114 tickets.

The most probable answer would be 114 tickets

PLZ MARK ME BRAINLIEST

4 0
3 years ago
Math binder is 3/4 inches thick how many binders will fit on a shelf 3 feet wide
Zigmanuir [339]

Answer:

48 binders

Step-by-step explanation:

36 inches

3/4 inches

flip around the fractio

36 x 4/3 = 48

OR 36 x 1.25=48

4 0
3 years ago
Other questions:
  • How many degrees does the hour hand of a clock turn between 3p.m and 7:30p.m
    8·2 answers
  • X - Y = 11<br> 2x + Y = 19<br><br> where do the lines cross
    12·1 answer
  • 33% of what number is 1.45
    7·2 answers
  • 1. Give the opposite of each number.
    15·1 answer
  • One angle of a triangle measures 132°. The other two angles are congruent. Enter and solve an equation to find the measure x of
    6·1 answer
  • Y’all I really need help with this, please help !!
    7·1 answer
  • (81m^6) 1/2 (Shift +6)
    14·1 answer
  • Y = −1 / 4 (x + 4) 2 −1 on a coordinate plane using its vertex, focus, and directrix.
    8·1 answer
  • david is ordering a photo book for his mom. The cost for a 7" x 9" book with 10 pages is 20$. Each additional page costs $1.50
    11·1 answer
  • A graph is shown below <br> what is the equation of the line in slope intercept form HELP ASAP
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!