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
GrogVix [38]
3 years ago
10

Solve the system by using elementary row operations on the equations. Follow the systematic elimination procedure

Mathematics
1 answer:
Umnica [9.8K]3 years ago
7 0

Answer:

The solution of the Given matrix

  ( x₁ ,    x ₂ ) = ( - 5 , 4 )

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given equations are  x₁+4 x₂ = 11 ...(i)

                                 2 x₁ + 7 x₂= 18 ...(ii)

The matrix form

                                A X = B

            \left[\begin{array}{ccc}1&4\\2&7\\\end{array}\right]  \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}11\\8\\\end{array}\right]

<u>Step(ii):-</u>

      \left[\begin{array}{ccc}1&4\\2&7\\\end{array}\right]  \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}11\\8\\\end{array}\right]

The Augmented Matrix form is

[AB] = \left[\begin{array}{ccc}1&4&11\\2&7&18\\\end{array}\right]

Apply Row operations,  R₂ → R₂-2 R₁

[AB] = \left[\begin{array}{ccc}1&4&11\\0&-1&-4\\\end{array}\right]  

The matrix form

                   \left[\begin{array}{ccc}1&4\\0&-1\\\end{array}\right]  \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}11\\-4\\\end{array}\right]

The equations are

                     x₁ + 4 x₂ = 11 ...(a)

                         - x ₂ = - 4

                            x ₂ = 4

Substitute   x ₂ = 4 in equation (a)

                      x₁ + 4 x₂ = 11

                      x₁ = 11 - 16

                        x₁ = -5

<u>Final answer</u>:-

The solution of the Given matrix

  ( x₁ ,    x ₂ ) = ( - 5 , 4 )

You might be interested in
Please help me with number 8 please!!
forsale [732]
The answer to number eight is
That it would have to reflect in the middle and it has Proportional angles.
7 0
2 years ago
What are the first five terms of the pattern with formula 3n + 4?
Leviafan [203]
In this equation we start by filling in the N with "1" then"2" then "3" and so on

3n+4=
3(1)+4=7
3(2)+4=10
3(3)+4=13
3(4)+4=16
4 0
2 years ago
Read 2 more answers
Which of the following is the volume of a square pyramid with a base of 6 in and a height of 7 in?
Karolina [17]
Volume = 1/3*a^2*h
So, V = (36*7)/3
          = 84
3 0
3 years ago
HELP
Yakvenalex [24]

Answer:

5. 50.3 m²

6. 113.1 cm²

7. 102.1 yards²

8.  50.3 yards²

9.  452.2 ft²

10.379.8 ft²

Step-by-step explanation:

Area of  a circle = nr²

The circumference of a circle = 2nr

n = pi = 22/7

r = radius

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

radius = diameter / 2

5. (22/7) x 4² = 50.3 m²

6.  (22/7) x 6² =113.1 cm²

7. radius = 11.4/2 = 5.7 yards

(22/7) x 5.7² =102.1 yards²

8. radius = 8/2 = 4 yards

(22/7) x 4² = 50.3 yards²

9. 2nr = 75.4 yards

2 x (22/7) x r = 75.4

to find r, divide both sides of the equation by 2 and 7/22

r = 12 ft

Area =  (22/7) x 12² = 452.2 ft²

10. 2nr = 69.1 yards

2 x (22/7) x r = 69.1

to find r, divide both sides of the equation by 2 and 7/22

r = 10.99 ft²

Area = (22/7) x 10.99² = 379.8 ft²

the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero

8 0
2 years ago
A coin has a diameter of 2.9 cm. If the coin is rolled through 25 complete revolutions, what distance will it travel?
nexus9112 [7]

Answer:

227.75 cm

Step-by-step explanation:

a coin (Circle) with diameter 2.9cm

(radius) r = diameter ÷ 2

r = 2.9cm ÷ 2

r = 1.45cm

1 complete revolutions (perimeter or circumference of a circle ) = 2πr

= 2 × π × r

where r = radius, π is a constant = 22/7

= 2 × 22/7 × 1.45

= 9.11cm

thus in one complete revolution the coin travels a distance of 9.11cm.

therefore in 25 complete revolutions the coin will travel a distance of = 25 × 9.11 cm = 227.75 cm.

The distance covered in complete 25 revolutions of a coin with diameter of 2.9 when it's rolled is = 227.75 cm

3 0
3 years ago
Other questions:
  • The table shown lists the atomic weight of the elements that begin with the letter c. What's the range of these
    10·1 answer
  • Divide -54 by -6 please
    11·1 answer
  • Which equation represents the line that passes through (-3,5) and is parallel to the graph of y= -2/3x+5
    9·1 answer
  • a circle has a radius of 4 an arc in this circle has a central angle of 288 what is the length of the arc
    13·1 answer
  • HELPPPPPPPPP!!! ASAPPPPP!!!!!!
    5·1 answer
  • Hello can anyone help me
    5·1 answer
  • Select all of the values.
    12·2 answers
  • Kendal has a 5-pound bag of flour that holds 1812 cups.
    12·1 answer
  • In the expression 85x - 99 what represents the coefficient?
    10·2 answers
  • Find the value of x<br> 6.1 - angles of polygons
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!