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
Rasek [7]
3 years ago
10

Solve the system by using a matrix equation

Mathematics
2 answers:
Sergeu [11.5K]3 years ago
6 0

Answer:

Option A is correct (17,11).

Step-by-step explanation:

6x - 9y = 3

3x - 4y =7

it can be represented in matrix form as\left[\begin{array}{cc}6&-9\\3&4\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}3\\7\end{array}\right]

A= \left[\begin{array}{cc}6&-9\\3&4\end{array}\right]

X= \left[\begin{array}{c}x\\y\end{array}\right]

B= \left[\begin{array}{c}3\\7\end{array}\right]

i.e, AX=B

or X= A⁻¹ B

A⁻¹ = 1/|A| * Adj A

determinant of A = |A|= (6*-4) - (-9*3)

                                    = (-24)-(-27)

                                    = (-24) + 27 = 3

so, |A| = 3

Adj A=  \left[\begin{array}{cc}-4&9\\-3&6\end{array}\right]

A⁻¹ =  \left[\begin{array}{cc}-4&9\\-3&6\end{array}\right]/3

A⁻¹ =  \left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right]

X= A⁻¹ B

X=  \left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right] *\left[\begin{array}{c}3\\7\end{array}\right]

X= \left[\begin{array}{c}(-4/3*3) + (3*7)\\(-1*3) + (2*7)\end{array}\right]

X= \left[\begin{array}{c}-4+21\\-3+14\end{array}\right]

X= \left[\begin{array}{c}17\\11\end{array}\right]

x= 17, y= 11

solution set= (17,11).

SVETLANKA909090 [29]3 years ago
5 0

Answer:

a. (17,11)

Step-by-step explanation:

The given system is ;

6x-9y=3

3x-4y=7

The augmented matrices is

\left[\begin{array}{ccc}6&-9&|3\\3&-4&|7\end{array}\right]

Divide Row 1 by 6

\left[\begin{array}{ccc}1&-\frac{3}{2}&|\frac{1}{2}\\3&-4&|7\end{array}\right]

Subtract 3 times Row 1 from Row 2

\left[\begin{array}{ccc}1&-\frac{3}{2}&|\frac{1}{2}\\0&\frac{1}{2}&|\frac{11}{2}\end{array}\right]

Divide Row 2 by \frac{1}{2}

\left[\begin{array}{ccc}1&-\frac{3}{2}&|\frac{1}{2}\\0&1}&|11\end{array}\right]

Add \frac{3}{2} times Row 2 to Row 1

\left[\begin{array}{ccc}1&0&|17\\0&1}&|11\end{array}\right]

Hence the solution is (17,11)

You might be interested in
Is 19/72 greater than 1/4
alina1380 [7]

Answer:

Yes

Step-by-step explanation:

\frac{1}{4}  =  \frac{1 \times 18}{4 \times 18}  =  \frac{18}{72}  \\  \because \: 19 > 18 \\  \therefore \:  \frac{19}{72}  >  \frac{1}{4}  \\

7 0
3 years ago
Read 2 more answers
Helppp!!!!! Plz. Mathhh
Julli [10]

Answer:

  1. 3n⁶
  2. 6n⁴
  3. 3x⁶
  4. 3x/y³
  5. 1/2ab⁵
  6. 3/4a⁴b⁶
  7. 1/uv⁴
  8. 2/u⁴b³
  9. 3x⁴y²/4
  10. 1
8 0
3 years ago
Find the value of x. Then find the angle measures of the triangle.
Vesnalui [34]
3x + 40 + x = 180
-40. -40
——————————-
4x. 140
—. ——-
4. 4

x = 35
4 0
3 years ago
Read 2 more answers
A block of concrete is 1m long, 50cm wild and 4cm thick. 1.calculate the volume of the block in cm3 .2.if 1cm has a mass of 2.7g
Nonamiya [84]

9514 1404 393

Answer:

  • 20,000 cm³
  • 54 kg

Step-by-step explanation:

1 m is 100 cm, so the volume is ...

  V = LWH

  V = (100 cm)(50 cm)(4 cm) = 20,000 cm³ . . . volume

__

The mass is ...

  (20,000 cm³)(2.7 g/cm³) = 54,000 g = 54 kg

The mass of the block is 54 kg.

7 0
3 years ago
8 divided by 6.403 round to the nearest tenths
lions [1.4K]
I believe the answer is 1.2
6 0
3 years ago
Read 2 more answers
Other questions:
  • Which is greater 8/10 or 63/100 ?
    7·1 answer
  • 9 Gregory thinks -6.9 is not a rational number because it is not a
    12·1 answer
  • -3r-8(8r+8)=-9(-4+9r)​
    9·1 answer
  • the arnold family arrived at the beach at 10:30 a.m. they spent 3¾ hours there.what time did they leave the beach?
    10·1 answer
  • Help please thank you so much
    10·1 answer
  • Suppose researchers test 100 college students, whose ages range from 18 to 23. They also test 100 people at a nearby community c
    8·1 answer
  • a restaurant offers a lunch special in which a customer can select from one of the 7 appetizers, one of the 10 entrees, and one
    12·1 answer
  • 2x - 7 < - 4x + 5 on graph and write the inequality.
    7·1 answer
  • Which relation is also a function (i can’t get this wrong please help) 15 points
    12·1 answer
  • Problem: The height, X, of all 3-year-old females is approximately normally distributed with mean 38.72
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!