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10. For the system of linear equation: (2x₁ + 3x₂ + x3 = -1 3x₁ + 3x₂ + x3 = 1 (2x₁ + 4x₂ + x3 = -2 a. find the coefficient matrix A and the augmented matrix [AL b. use Gauss Jordan method to find the inverse of the coefficie c. find the solution set of 'he system using Matrix inverse Me-
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a. Coefficient matrix A:
A = [[2, 3, 1],
[3, 3, 1],
[2, 4, 1]]
Augmented matrix [AL]:
[A|b] = [[2, 3, 1, -1],
[3, 3, 1, 1],
[2, 4, 1, -2]]
b. The resulting matrix will be [I|A^(-1)], where A^(-1) is the inverse of the coefficient matrix A.
c. The resulting vector [x1, x2, x3] represents the solution set of the system of linear equations.
a. The coefficient matrix A and the augmented matrix [A|b] for the given system of linear equations are as follows:
Coefficient matrix A:
A = [[2, 3, 1],
[3, 3, 1],
[2, 4, 1]]
Augmented matrix [AL]:
[A|b] = [[2, 3, 1, -1],
[3, 3, 1, 1],
[2, 4, 1, -2]]
b. To find the inverse of the coefficient matrix A using the Gauss-Jordan method, we perform elementary row operations until A is transformed into an identity matrix [tex][I|A^{(-1)][/tex].
Gauss-Jordan elimination steps:
Step 1: Perform row operations to convert the first column of A to [1, 0, 0]:
R1' = R1/2
R2' = R2 - (3/2)R1
R3' = R3 - R1
Step 2: Perform row operations to convert the second column of A to [0, 1, 0]:
R2'' = R2''/3
R1'' = R1'' - (3/2)R2''
R3'' = R3'' - (3/2)R2''
Step 3: Perform row operations to convert the third column of A to [0, 0, 1]:
R3''' = R3'''/2
R1''' = R1''' - R3'''
R2''' = R2''' - R3'''
The resulting matrix will be[tex][I|A^{(-1)][/tex], where [tex]A^{(-1)[/tex] is the inverse of the coefficient matrix A.
c. Once we have the inverse matrix A^(-1), we can find the solution set of the system of linear equations by multiplying A^(-1) with the augmented matrix [A|b]:
[A|b] [tex]\times[/tex] [tex]A^{(-1)[/tex] = [x1, x2, x3]
The resulting vector [x1, x2, x3] represents the solution set of the system of linear equations.
Note: To provide the numerical values for the inverse matrix [tex]A^{(-1)[/tex] and the solution set, the calculations need to be performed manually using the given coefficients of the equations.
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Which function has the largest maximum? (1 point)
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Answer:
(4, -7) thats the largest maximum
the force keeping the moon in its orbit round the earth is inversely proportional to the square of the distance from the earth.if F =6×10^5KN and R =8×10^8.find the equation connecting Fand R.
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9514 1404 393
Answer:
F = 3.84×10^23/R²
Step-by-step explanation:
No units are given for distance, so we cannot give a constant of proportionality that has suitable units.
The general form for inverse square variation is ...
F = k/R²
Then the value of k can be found from ...
k = F·R² = (6×10^5)(8×10^8)^2 = 3.84×10^23
The formula relating the given F and R is ...
F = 3.84×10^23/R²
Tasha is mixing red and white paint to make pink paint. She uses 1/3 pint of red paint to make 1/2 pint of pink paint. How much red paint would she use to make 3 1/2 pints of pink paint?
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Answer:
2 1/3
Step-by-step explanation:
Suppose tie structural equations of 3 economies are given as: AD = C +10 C =250 + 0.8Y I0 = 200 Find the equilibrium values of Y and C
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Answer:
Step-by-step explanation:
LMAFOOOOOOOOOOOOOOOOOOOOOO
you get a haircut that costs $23. You want to tip the barber 10%. How much tip will you leave him?
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Answer:
$2.30
Step-by-step explanation:
Multiply 23 by .10 to get 2.3
2.3 is 2 dollars and 30 cents
Answer:
$2.30
Step-by-step explanation:
multiply 23 by the decimal form of 10% (0.10)
23*0.10=2.3
PLEASE HELP I WILL MARK YOU BRAINIEST
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Answer:
The answer is (D) y < 4
Answer:
D. y < 4 im pretty sure sorry if its wrong..
What value of x makes the following equation true x + 10 = 18
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x+10-10=18-10
x=8
Step-by-step explanation:
The value should be
X=18-10= 8
X=8 Answer
Does (2, 3) make the inequality 2x + 5y < 20 true?
yes
no
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Answer:
Yes
Step-by-step explanation:
The left side 19 is less than the right side 20 , which means that the given statement is always true.
find the least common multiple of 16,30,36 no links or file
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9514 1404 393
Answer:
720
Step-by-step explanation:
The LCM of these numbers will have every factor that is part of these numbers.
16 = 2^4
30 = 2 × 3 × 5
36 = 2^2 × 3^2
So, the LCM will have factors of 2^4, 3^2, and 5:
LCM(16, 30, 36) = 2^4 × 3^2 × 5 = 720
720 = 16×45 = 30×24 = 36×20
The least common multiple is 720.
Mark hsa a square photo with an area of 9cm squared.
He enlarged the photo to have an area of 36 cm squared
To do this the length of each side was multiplied by a factor of
two three four five or six?
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Answer:
4
Step-by-step explanation:
36/9=4
Which number sentence is true?
A. 82 < |-82|
B. |-82| < |-83|
C. |-83| < |83|
D. |82| > |-83|
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Answer:
Given:
radius = 8
Volume of a sphere = 4/3 * π * r³
V = 4/3 * 3.14 * 8³
V = 1.33 * 3.14 * 512
V = 2,138.21 cubic unit
Step-by-step explanation: Hope This Helped!!
Mr Soto bought some dvds each DVD cost 13.55 if Mr Soto did not spend more Thales 75$ which inequality could be used to find d the number of DVDs Mr. Soto bought
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Answer:
c
Step-by-step explanation:
C is the only equality that no matter what, the value would be $75 or less
Pls help ASAP. Pls and thx.
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Answer:
(assuming the. values are the shaded areas)
area = x^2 + 2x +2
perimeter = 4x + 8
Step-by-step explanation:
you have all the side except the side of the 2 squares at the top.
The squares are 1 unit on each side because the area of the 2 slender rectangles on each side is x.
So the area is x^2 + x + x + 1 + 1
The perimeter is 1+x+1+1+1+x+1+1+1+x+1+x
(starting from the lower left side and walking around the perimeter clockwise)
Mona solved an equation incorrectly, as shown below:
Step 1: 5x = 30
Step 2: x = 30 − 5
Step 3: x = 25
Which statement best explains why Step 2 is incorrect in Mona's solution?
She did not add 5 to 30.
She did not divide 30 by 5.
She did not multiply 30 by 5.
She did not multiply 30 five times.
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Answer:
She did not add 5 to 30. ... Mona subtracted 5 where she should have divided 5.
Step-by-step explanation:
Answer:
B. She did not divide 30 by 5
Step-by-step explanation:
This is the only way to cancel out the 5 and get the variable alone
The perimeter of the figure below is 54.9 in. Find the length of the missing side.
5.9 in
5.9 in
?
7-3 in
7.3 in
7.3 in
7.3 in
7.3 in
(Note: diagram is NOT to scale)
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What is the height of the ball after 5 seconds in feet?
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Answer:32
Step-by-step explanation:
i think the answer will be 32 feet
I need help. This is due later today.
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Answer:
the first one
Step-by-step explanation:
What is the radius of a circle that has an approximate circumference of 81.64 meters? (Use 3.14 for ).
r =
m
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2r(3.14) = 81.64
6.28r = 81.64
r = 13
12.99m
Answer:
r=13
Step-by-step explanation:
81.64/3.14=26(diameter)
26/2=13(radius)
Help?
The circumference of a circle is 25 cm. Find the length of the radius
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Answer:
3.99
Step-by-step explanation:
Divide circumference by pi. The answer will be the circles diameter and then divide this by 2 for the radius
45,000 mL=
I really need this answer just one more Time lol
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Answer:
45,000 mL (Milliliters) = 45 L (Liters)
Explanation:
The word milliliters is made up of two words, "milli" and "liter"
"Milli" means a thousand, chiefly denoting a factor of one thousandth.
That means one milliliter is one thousandth of a liter
Select the correct comparison.
Set A
Set B
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A single line of four cats one behind the other walks towards and head-on into a single line of five cats walking in the opposite direction. When two of the nine cats meet, they both switch directions and then continue walking. How many meetings take place?
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Answer:LLLLLLLLLLLLLL
Step-by-step explanation:
LLLLLLLLLl
Answer:
4
Step-by-step explanation:
There are just 4
I need some help with this question. Can someone help me pls???
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Answer:
24yd I think thats the answer
Answer:
B
Step-by-step explanation:
6 * 4 = 24
[ (9 - 6) * 4 ] / 2 = 6
24 + 6 = 30
(1\6-1)(3-2/5)-(1/3-1/2)
Answers
Answer:
2 1/3 (simplified)
Step-by-step explanation:
(1/6 - 1) = -5/6
(1 = 6/6)
(3 - 2/5) = 2 3/5
[3= 18 (3 * 6)]
(1/3 - 1/2) = -1/6
(you can change both of the denominators to 6 by multiplying them both by 3 / 2
So the equation now is
(-5/6)(2 3/5) - (-1/6)
-5/6 * 2 3/5 = 2 1/6 (simplified)
2 1/6 - -1/6 = 2 1/3 (simplified)
HELP FAST PLZ
The same house costing $500,000 with the 15-year mortgage and the APR of
4.5% would have what amount for its first month's principal payment?
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Answer:
Step-by-step explanation:
How much would the mortgage payment be on a $500K house? Assuming you have a 20% down payment ($100,000), your total mortgage on a $500,000 home would be $400,000. For a 30-year fixed mortgage with a 3.5% interest rate, you would be looking at a $1,796 monthly payment.
6. The base of a pyramid is a triangle whose base is 11 yards and height is 19
yards. Determine the volume of the pyramid, if its height is 7 yards. Round
your answer to two decimal places.
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Because volume= lwh/3
Solve 3/4 = j- 1/2 j=
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Answer:
3/8
Step-by-step explanation:
Solve for the value of r.
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Answer:
r = 20
Step-by-step explanation:
4r - 5 + 105 = 180
4r + 100 = 180
4r = 80
r = 20
Escribe 2 ejemplos de enunciados que establezcan una regla de correspondencia que represente una función y
represéntala con un diagrama de flechas.
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Answer:
Correspondencia entre conjuntos:
a) Inyectiva: es cuando a cada imagen en el conjunto de llegada le corresponde un único origen, es decir, a distintos elementos del conjunto inicial, les corresponden distintos elementos del conjunto final.
b) Sobreyectiva: es si todos los elementos del conjunto final tienen al menos una correspondencia del conjunto inicial
c) Biyectiva: es cuando la correspondencia es inyectiva y sobre inyectiva a la vez
Correspondencia unívoca : es una correspondencia donde cada elemento del conjunto origen se corresponde con solo un elemento del conjunto de llegada.
Correspondencia biunívoca es cuando a cada elemento del conjunto origen se corresponde con solo un elemento del conjunto llegada, y viceversa
Step-by-step explanation: