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
ahrayia [7]
1 year ago
15

Solve the system of equations by using the inverse of the coefficient matrix of the equivalent matrix equation.

Mathematics
1 answer:
Alinara [238K]1 year ago
4 0

The solution for the given system of equations x + 8y = -37, 4x + 8y = -52 is \left[\begin{array}{ccc}&5&\\\\&4&\end{array}\right]

Given,

System of equations as,

x + 8y = -37

4x + 8y = -52

We have to solve this by using the inverse of coefficient matrix of the equivalent matrix equation.

That is,

A=\left[\begin{array}{ccc}a&&b\\\\c&&d\end{array}\right]

A^{-1} =\frac{1}{ad -bc} \left[\begin{array}{ccc}d&&-b\\\\-c&&a\end{array}\right]

Now we can solve the equations.

Here we have,

x + 8y = -37

4x + 8y = -52

Now in matrix form,

\left[\begin{array}{ccc}1&&8\\\\4&&8\end{array}\right]  \left[\begin{array}{ccc}&x&\\\\&y&\end{array}\right] =\left[\begin{array}{ccc}&-37&\\\\&-52&\end{array}\right]

      A               X                  B

We know that,

A^{-1} =\frac{1}{ad -bc} \left[\begin{array}{ccc}d&&-b\\\\-c&&a\end{array}\right]

Therefore,

A^{-1} = \frac{1}{(1X8)-(4X8)} \left[\begin{array}{ccc}8&&-8\\\\-4&&1\end{array}\right]

       =\frac{1}{8-32} \left[\begin{array}{ccc}8&&-8\\\\-4&&1\end{array}\right]

       =\frac{1}{-24} \left[\begin{array}{ccc}8&&-8\\\\-4&&1\end{array}\right]

       =\left[\begin{array}{ccc}\frac{-8}{24} &&\frac{8}{24} \\\\\frac{4}{24} &&\frac{-1}{24} \end{array}\right]

Then,

\left[\begin{array}{ccc}&x&\\\\&y&\end{array}\right] ==\left[\begin{array}{ccc}\frac{-8}{24} &&\frac{8}{24} \\\\\frac{4}{24} &&\frac{-1}{24} \end{array}\right]  \left[\begin{array}{ccc}&\frac{37}{52} &\\\\\end{array}\right]

                =\frac{1}{24} \left[\begin{array}{ccc}-8&&8\\\\4&&-1\end{array}\right]\left[\begin{array}{ccc}&\frac{37}{52} &\\\\\end{array}\right]

                =\frac{1}{24} \left[\begin{array}{ccc}(-8X37)+(8X52)\\\\(4X37)+(-1X52)\end{array}\right]

               =\frac{1}{24} \left[\begin{array}{ccc}-296+416\\\\148-52\end{array}\right]

               =\frac{1}{24} \left[\begin{array}{ccc}120\\\\96\end{array}\right]

               =\left[\begin{array}{ccc}\frac{120}{24} \\\\\frac{96}{24} \end{array}\right]

              =\left[\begin{array}{ccc}5\\\\4\end{array}\right]

That is \left[\begin{array}{ccc}x\\\\y\end{array}\right] =\left[\begin{array}{ccc}5\\\\4\end{array}\right]

Learn more about matrix equations here: brainly.com/question/27799804

#SPJ4

The question is incomplete. Completed question is given below:

Solve The System Of Equations By Using The Inverse Of The Coefficient Matrix Of The Equivalent Matrix Equation.

x + 8y = -37

4x + 8y = -52

You might be interested in
Need help finding the measure of the arc or angle indicated
evablogger [386]

Answer:

70 degrees

Step-by-step explanation:

6 0
2 years ago
On average, water flows over a particular water fall at a rate of 2.08 x 105 cubic feet per second. One cubic foot of water weig
34kurt

Answer:

  5.61×10^8 ton/day

Step-by-step explanation:

  (2.08×10^5 ft³/s)·(8.64×10^4 s/day)·(6.24×10^1 lb/ft³)/(2×10^3 lb/ton)

  = (2.08·8.64·6.24/2)×10^(5+4+1-3) ton/day

  ≈ 56.07×10^7 ton/day

  ≈ 5.61×10^8 ton/day

_____

We have expressed the answer using 3 significant digits, to match the precision of the rate and weight.

4 0
3 years ago
The sale price of a used car is $4,160 after a 35% discount. What is the original price of the car?
erik [133]

Answer: The original price was $6,400

Step-by-step explanation: To find the original price, divide the sale price by 1 minus the discount rate:  4160 / (1- 0.35) =  4160 / 0.65 = 6400

mark brainliest?? plz :)

3 0
3 years ago
The walls of a farm silo form a hexagonal prism as shown. What is the volume of the​ silo?
Valentin [98]
I think this is what you meant you meant silo or Solid if you meat solid the answer is there in the picture

3 0
3 years ago
Select the correct answer.
Umnica [9.8K]
I believe this would be a contingent discount. Contingent discounts are granted to a buyer when they satisfy certain requirements. In this case, the requirement is to have a minimum purchase of $500. Thus, that would make it a contingent discount.
The other's are incorrect.
A membership discount requires you to have a membership. 
A straight discount is basically present value of future cash flow without compounding. (Business Dictionary Definition)
A bulk purchase discount is a financial incentive for regular shoppers or businesses that buy things in bulk.
8 0
3 years ago
Read 2 more answers
Other questions:
  • The perimeter of a triangle is 84. The longest side is 7 meters less than twice the length of the shortest side, x. The middle s
    8·1 answer
  • the two lines graphed below are perpendicular. if the slope of the solid line is 3/4, what is the slope of the dashed line?
    5·2 answers
  • Subtract these polynomials (3x^2x+4)-(x^2+2x+1)
    15·2 answers
  • If f(x) = 3x and g(x) = 3x + 1 + 6. Describe the transformations from f(x) to g(x).
    14·2 answers
  • PLZZZZ HELP!!!!!!!
    8·1 answer
  • When is it better to use a table in math
    6·1 answer
  • Please answer TwT I need it fasssssssst
    14·2 answers
  • What answee is it?? :))))
    12·2 answers
  • Right answer gets brainlyest
    7·1 answer
  • A simple random sample of size individuals who are currently employed is asked if they work at home at least once per week. Of t
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!