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
julia-pushkina [17]
3 years ago
6

Create a matrix for this system of linear equations, The determinant of the coefficient matrix is

Mathematics
1 answer:
marin [14]3 years ago
3 0

Answer:  The determinant of the coefficient matrix is -15 and x = 3, y = 4, z = 1.

Step-by-step explanation:  The given system of linear equations is :

2x+y+3z=13~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x+2y=11~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\3x+z=10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)

We are given to find the determinant of the coefficient matrix and to find the values of x, y and z.

The determinant of the co-efficient matrix is given by

D=\begin{vmatrix}2 & 1 & 3\\ 1 & 2 & 0\\ 3 & 0 & 1\end{vmatrix}=2(2-0)+1(0-1)+3(0-6)=4-1-18=-15.

Now, from equations (ii) and (iii), we have

x+2y=11~~~~~\Rightarrow y=\dfrac{11-x}{2}~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)\\\\\\3x+z=10~~~~~~\Rightarrow z=10-3x~~~~~~~~~~~~~~~~~~~~~~~~~(v)

Substituting the value of y and z from equations (iv) and (v) in equation (i), we get

2x+y+3z=13\\\\\Rightarrow 2x+\dfrac{11-x}{2}+3(10-3x)=13\\\\\Rightarrow 4x+11-x+60-18x=26\\\\\Rightarrow -15x+71=26\\\\\Rightarrow -15x=26-71\\\\\Rightarrow -15x=-45\\\\\Rightarrow x=3.

From equations (iv) and (v), we get

y=\dfrac{11-3}{2}=4,\\\\z=10-3\times3=1.

Thus, the determinant of the coefficient matrix is -15 and x = 3, y = 4, z = 1.

You might be interested in
Find the length of a line segment with endpoints of –9 and 7.
madreJ [45]

Answer:

c 16

Step-by-step explanation:

7 0
3 years ago
What is 4/7 x 3/4 and 1 2/3 x 1/5?
Elena-2011 [213]
Answer: 3/7 and 12/15

5 0
3 years ago
Read 2 more answers
Muffins are packed and sold in boxes of 4. How many boxes are needed to pack 260 muffins?
Volgvan

Answer:

65 boxes

Step-by-step explanation:

Im not sure how to explain other then say all you do is divide 260 and 4

I hope this helped!

Good luck!

If i did help maybe you could help me by giving me brainliest!?

Thanks! <3

5 0
3 years ago
Indicate the equation of the line, in standard form, that passes through (2, -4) and has a slope of 3/5. Enter your answer into
yulyashka [42]

The equation of the line is  y = (3/5)x + 26/5

<u>Step-by-step explanation:</u>

  • The line passes through the point (2,-4).
  • The line has the slope of 3/5.

To find the equation of the line passing through a point and given its slope, the slope-intercept form is used to find its equation.

<u>The equation of the line when a point and slope is given :</u>

⇒ (y-y1) = m(x-x1)

where,

  • m is the slope of the line.
  • (x1,y1) is the point (2.-4) in which the line passes through.

Therefore, the equation of the line can be framed by,

⇒ (y-(-4)) = 3/5  (x-2)

⇒ (y+4) = 3/5(x-2)

Take the denominator 5 to the left side of the equation.

⇒ 5(y+4) = 3(x-2)

Now, multiply the number outside the bracket to each term inside the bracket.

⇒ 5y+20 = 3x -6

⇒ 5y = 3x-26

Divide by 5 on both sides of the equation,

⇒ y = (3/5)x + 26/5

Therefore, the equation of the line is  y = (3/5)x + 26/5

4 0
3 years ago
Read 2 more answers
(3.6 x 10^-5) divided by (1.8 x 10^2) <br> Write your answer in standard form
Genrish500 [490]

Answer:

The standard form of  is 0.0000002

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • Use the following terms to describe the challenging environment of west and central Africa : Deforestation, desertification, mal
    9·1 answer
  • Fill in the table using this function rule
    11·1 answer
  • The temperature at 10 AM is 12°F. The temperature at 6 AM was -7°F. How many degrees did the temperature rise?
    5·2 answers
  • adam's types 88 words per minute.How many words per second can adam type? round to the nearest hundredth
    12·1 answer
  • As shown in the image below, triangle ABC is reflected onto its image. А B с С" A Which of the following lines represents the li
    7·1 answer
  • Which of these is a trinomial?
    9·2 answers
  • Will give Brainliest for correct answer! :)
    7·2 answers
  • Which logarithmic equation is equivalent to the exponential below ? e^5x=6
    13·1 answer
  • Add 4 to the sum of K and 8
    11·1 answer
  • 15 is what percentage of 30
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!