solve the following system of equations using lu factorization with partial pivoting: 2x1−6x2−x3=−38 −3x1−x2 7x3=−34 −8x1 x2−2x3=−40
Answers
x = [2; 5; 1] is the solution to the given system of equations 2x1−6x2−x3=−38 −3x1−x2 7x3=−34 −8x1 x2−2x3=−40 using LU factorization with partial pivoting.
To solve the system of equations using LU factorization with partial pivoting, we first write the system in matrix form as:
A*x = b
where A is the coefficient matrix:
A = [2 -6 -1; -3 -1 7; -8 1 -2]
x is the vector of unknowns:
x = [x1; x2; x3]
and b is the vector of constants:
b = [-38; -34; -40]
We then perform LU factorization with partial pivoting on A to get:
P*A = L*U
where P is the permutation matrix that represents the row exchanges done during the factorization, L is the lower triangular matrix with ones on the diagonal, and U is the upper triangular matrix. We can solve the system using the following steps:
Step 1: Perform partial pivoting to interchange the first and third rows of A:
A = [−8 1 −2; −3 −1 7; 2 −6 −1]
P = [0 0 1; 0 1 0; 1 0 0]
Step 2: Compute the LU factorization of A:
L = [1 0 0; −0.25 1 0; −0.25 0.8571 1]
U = [−8 1 −2; 0 −0.75 6.5; 0 0 −3.1429]
Step 3: Solve Ly = Pb for y:
Pb = [−40; −34; −38]
y = [−38; 0.25; 1.2857]
Step 4: Solve Ux = y for x:
x = [2; 5; 1]
Therefore, the solution to the system of equations is:
x1 = 2
x2 = 5
x3 = 1
Note: The LU factorization with partial pivoting is a numerical method for solving systems of linear equations. It is not always necessary to use this method for small systems like the one in this example, but it can be useful for larger systems or for matrices that are difficult to solve using other methods.
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Related Questions
Ms. Armstrong purchased a car for $20,000. After 4 years, the car was only worth $8,000. Write an equation in slope intercept form that can be used to find the value of the car y, after x number of years.
Answers
Answer:
$20,000=4x
Step-by-step explanation:
First if we want to find out how much the price of the car went down we would have to find out how much the price went down by subtracting $20,000 by $8,000. I got 12,000. Then we have to find out how much the price went down every year. So, $12,000 ÷ 4 = $3,000. So, in 4 years the price went down $3,000 dollars every year
The sum of 19.3 and a number is 30.4. Which equation can be used to solve the problem? n minus 19.3 = 30.4 19.3 + n = 30.4 19.3 minus n = 30.4 n + 30.4 = 19.3
Answers
Answer:
Below.
Step-by-step explanation:
19.3 + n = 30.4
Answer: B (they are correct)
Step-by-step explanation:
Edge 2020
I NEED PART C QUICK
Triangle PQR is transformed to triangle P′Q′R′. Triangle PQR has vertices P(8, 0), Q(6, 2), and R(−2, −4). Triangle P′Q′R′ has vertices P′(4, 0), Q′(3, 1), and R′(−1, −2).
Plot triangles PQR and P′Q′R′ on your own coordinate grid.
Part A: What is the scale factor of the dilation that transforms triangle PQR to triangle P′Q′R′? Explain your answer. (4 points)
Part B: Write the coordinates of triangle P′′Q′′R′′ obtained after P′Q′R′ is reflected about the y-axis. (4 points)
Part C: Are the two triangles PQR and P′'Q′'R′' congruent? Explain your answer. (2 points)
Answers
(4a + 2)(6a^2-a + 2)
Answers
Answer:
24a^3+8a^2+6a+4
Step-by-step explanation:
(4a+2)(6a^2-a+2)
Distribute parentheses
6a^2+4a(-a)+4a :2+2 :6a^2+2(-a)+2 :2
Apply minus-plus rules
=4 6a^2a-4aa+4 :2a+2 6a^2-2+2 .2
Scenario 2 Magnifi Co. produces a high-end amplifier for musical aficionados. Historically, only 85% of the 200 amplifiers produced per month on average have met the company's demanding standards for
Answers
Scenario 2 Magnifi Co. produces a high-end amplifier for musical aficionados. Historically, only 85% of the 200 amplifiers produced per month on average have met the company's demanding standards for quality control. Suppose a random sample of 50 amplifiers is taken from a month's production..
What is the probability that less than 40 of the amplifiers will meet the company's quality standards? b) What is the probability that between 40 and 45 inclusive of the amplifiers will meet the company's quality standards? c) What is the probability that more than 45 of the amplifiers will meet the company's quality standards? a) In order to solve for the probability that less than 40 amplifiers will meet the company's quality standards, we can use the binomial distribution formula: P(X < 40) = Σi=0^39 C(50, i) (0.85)i(1-0.85)50-i
This can be solved using a computer, calculator, or by using a binomial probability table. Using a binomial table, we can find that P(X < 40) = 0.024. Therefore, there is a 0.024 probability that less than 40 amplifiers will meet the company's quality standards. b) To solve for the probability that between 40 and 45 amplifiers inclusive will meet the company's quality standards, we can use the binomial distribution formula again. We need to solve for P(40 ≤ X ≤ 45): P(40 ≤ X ≤ 45) = Σi=40^45 C(50, i) (0.85)i(1-0.85)50-i This can also be solved using a computer, calculator, or binomial table. Using a binomial table, we can find that P(40 ≤ X ≤ 45) = 0.435. Therefore, there is a 0.435 probability that between 40 and 45 amplifiers inclusive will meet the company's quality standards. c) To solve for the probability that more than 45 amplifiers will meet the company's quality standards, we can use the binomial distribution formula one more time. We need to solve for P(X > 45): P(X > 45) = Σi=46^50 C(50, i) (0.85)i(1-0.85)50-i Once again, this can be solved using a computer, calculator, or binomial table. Using a binomial table, we can find that P(X > 45) = 0.056. Therefore, there is a 0.056 probability that more than 45 amplifiers will meet the company's quality standards.Overall, it can be concluded that the probability that less than 40 amplifiers will meet the company's quality standards is low, the probability that between 40 and 45 amplifiers inclusive will meet the company's quality standards is relatively high, and the probability that more than 45 amplifiers will meet the company's quality standards is relatively low.
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Solve for x.
Use the quadratic formula.
2x2−9x+8=0
Enter the solutions, in simplified radical form, in the boxes.
x =
or x =
Answers
\(\\ \rm\rightarrowtail 2x^2-9x+8=0\)
\(\\ \rm\rightarrowtail x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\)
\(\\ \rm\rightarrowtail x=\dfrac{9\pm\sqrt{81-64}}{4}\)
\(\\ \rm\rightarrowtail x=\dfrac{9\pm\sqrt{27}}{4}\)
\(\\ \rm\rightarrowtail x=\dfrac{9\pm3\sqrt{3}}{4}\)
John is creating a Thanksgiving display at the store where he works, using only canned pumpkin and canned green beans. He needs to maintain a ratio of pumpkin to green beans of 5 to 2. If he wants to use a total of 126 cans, how many cans of green beans should he use?
please help me lol
Answers
Answer:
90 pumpkin and 36 green beans
Step-by-step explanation:
Because there is a total of 7 parts (5+2) and I divided 126 by 7 and then put five of the 18ns (the quotient of 126 and 7) for pumpkins (so... multiply 18 by 5) then the other to times 18 is 36. And if you add them together, they equal 126.
Answer:
9 cans
Step-by-step explanation:
126/7=18
18/2=9
so 9 is the answer
(plz mark brainlyist)
pls help asap
What are some advantages of using coins and paper money as currency? What are some disadvantages of using the barter system
Answers
Disadvantages of barter system:
Lack of double coincidence of wants.
Lack of a common measure of value.
Indivisibility of certain goods.
Difficulty in making deferred payments.
Difficulty in storing value.
Solve -319 + x) = 33
Answers
Answer:
x = 352
Step-by-step explanation:
Move all terms not containing x to the right side of the equation.
Answer:
x=352
Step-by-step explanation:
-319+x=33
+319 +319
x=352
Recent difficult economic times have caused an increase in the foreclosure rate of home mortgages. Statistics from the Penn Bank and Trust Company show their monthly foreclosure rate is now one loan out of every 136 loans. Last month the bank approved 300 loans.A. How many foreclosures would you expect the bank to have last month?B. What is the probability of exactly two foreclosures?C. What is the probability of at least one foreclosure?
Answers
Probability is a measure of the likelihood of an event occurring.
A. To find how many foreclosures to expect, we can use the expected value formula: E(X) = np, where X is the number of foreclosures, n is the number of loans, and p is the foreclosure rate. Substituting the given values, we have E(X) = (300)(1/136) ≈ 2.21. Therefore, we can expect about 2 foreclosures last month.
B. To find the probability of exactly two foreclosures, we can use the Poisson distribution with parameter λ = E(X) = 2.21. The probability mass function of the Poisson distribution is given by P(X = k) = (e^(-λ) * λ^k) / k!, where k is the number of foreclosures. Substituting k = 2 and λ = 2.21, we have P(X = 2) = (e^(-2.21) * 2.21^2) / 2! ≈ 0.244. Therefore, the probability of exactly two foreclosures is about 0.244.
C. To find the probability of at least one foreclosure, we can use the complement rule: P(X ≥ 1) = 1 - P(X = 0). Since the foreclosure rate is one out of every 136 loans, the probability of not having a foreclosure in a single loan is (135/136). Therefore, the probability of not having a foreclosure in 300 loans is (135/136)^300 ≈ 0.427. Substituting this value into the complement rule, we have P(X ≥ 1) = 1 - 0.427 ≈ 0.573. Therefore, the probability of at least one foreclosure is about 0.573.
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the ratio of the numbers of sides of two polygons is 1:2. if each interior angle of the first polygon is 120degree, then the measure of each interior angle of the second polygon is
Answers
Answer:
150°
Step-by-step explanation:
You want to know the measure of an interior angle of a regular polygon that has twice as many sides as one with an interior angle of 120°.
Exterior angleThe exterior angle of a regular polygon is the supplement of the interior angle. The polygon with an interior angle of 120° has an exterior angle of ...
180° -120° = 60°
The sum of exterior angles is 360°, so there must be 360°/60° = 6 of them. In the polygon with twice as many sides, there will be twice as many exterior angles, so each will measure 360°/12 = 30°.
Interior angleThe corresponding interior angle is ...
180° -30° = 150°
The measure of each interior angle of the second polygon is 150°.
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A marketing survey involves product recognition in New York and California. Of 198 New Yorkers surveyed, 51 knew the product while 74 out of 301 Californians knew the product. At the 2.5% significance level, use the critical value method to test the claim that the recognition rates are different in the states. Enter the smallest critical value. (Round your answer to nearest hundredth.)
Answers
The smallest critical value is -1.96 at the 2.5% significance level.
To test the claim that the recognition rates are different in New York and California, we can use a two-sample z-test for proportions.
The null hypothesis is that the proportion of people who recognize the product in New York is equal to the proportion in California, while the alternative hypothesis is that they are different.
Let p1 be the proportion of people who recognize the product in New York, p2 be the proportion in California, and p be the pooled proportion. Then:
p1 = 51/198 = 0.2576
p2 = 74/301 = 0.2458
p = (51+74)/(198+301) = 0.2514
The test statistic is given by:
z = (p1 - p2) / sqrt(p*(1-p)*(1/198 + 1/301))
z = (0.2576 - 0.2458) / sqrt(0.2514*(1-0.2514)*(1/198 + 1/301))
z = 1.1143
Using a significance level of 2.5%, the critical value for a two-tailed test is ±1.96.
Since our test statistic falls within this range, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the recognition rates are different in New York and California.
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One gallon of water weighs 8. 34 pounds. How much does 6 gallons of water weigh? Show your work, including labeling your answer with the appropriate units of measure
Answers
According to the given situation, 6 gallons of water weighs 50.04 pounds.
The United States and certain other nations frequently use the gallon as a unit of volume measurement. Although there are other types of gallons, the U.S. gallon, which is equivalent to 128 fluid ounces or 3.785 liters, is the most often used. It is used to calculate the volume of fluids like milk, water, petrol, and other substances. The word gallon is shortened to "gal."
One gallon of water weighs 8.34 pounds. To find the weight of 6 gallons of water, we can multiply the weight of one gallon by 6:
Weight of 6 gallons of water = 6 x 8.34 pounds
On simplifying we get:
Weight of 6 gallons of water = 50.04 pounds
Therefore, 6 gallons of water weighs 50.04 pounds.
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A trinomial with a leading coefficient of 3 and a constant term of -5 Choose 1 answer: (A) 3m^(2)+m-5 (B) -5m^(2)+4m+3 (C) 3m^(2)-5m+1 (D) 3m^(2)-5.
Answers
A trinomial is a polynomial with three terms that has a leading coefficient of 3 and a constant term of -5 is
3m²+m-5
Here the degree of the trinomial is 2, so the leading coefficient is the coefficient of the term with m², which is 3.
The constant term is the term without a variable, which is -5
To find the coefficient of middle term of the trinomial, formula is:
coefficient of middle term =
(sum of the coefficients of the first and last terms)
2
The sum of the coefficients of the first and last terms is 3 - 5 = -2.
Dividing by 2, we get -1 as the coefficient of the middle term.
Putting all of this together, we can write the trinomial as: 3m² +m - 5
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What do you add to 2 3/7 to make 4
&
What do you add to 5 4/9 to make 7
Answers
Hope this helps, have a nice day!!!
Our answers are
1 4/7 and 1 5/9
i need help somebody please
Answers
Answer 24a + 6
Step-by-step explanation:
8 + 18a -2 + 6a
18a + 6a = 24a
8 - 2 = 6
24a + 6
Find the value of the variables
Answers
Answer:
Step-by-step explanation:
\(\text{Since there are two 45 degree angles.}\\ \\ a=4\sqrt{2}\\ \\ \text{By the Pythagorean Theorem }c^2=a^2+b^2,\text{ and in this case a=b so }\\ \\ c^2=2(4\sqrt{2})^2\\ \\ c^2=2(16)2\\ \\ c^2=64\| \\ c=\sqrt{64}\\ \\ c=8\)
A company finds that when they pay employees more, the employees are more productive. How would you classify these events, based on this finding?
Independent
Dependent
Answers
Based on the finding that paying employees more results in increased productivity, we can conclude that the event of paying employees more is the independent variable, while the event of increased productivity is the dependent variable.
This means that paying employees more is the cause or predictor of increased productivity, while increased productivity is the effect or outcome of paying employees more. In mathematical terms, we can represent this relationship as:
Increased Productivity = f(Paying Employees More)
Where "f" is a function that maps the level of Paying Employees More to the level of Increased Productivity. The function can take different forms depending on the nature of the relationship between the two events. For example, it could be a linear function, where the increase in productivity is proportional to the increase in pay.
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Two forces of 8.6 newtons and 3.5 newtons act simultaneously on an object. The angle between the two forces is 58°. Find the magnitude of the resultant, to the nearest 10th of a newton.
Answers
Hence, the force that results has a magnitude of about 10.3 newtons (rounded to the nearest 10th of a newton).
What does magnitude imply?"How much of a quantity" is the definition of magnitude. For instance, the amount of data can be utilized for assessing the speeds of a car and a bicycle. In addition, it can be used to express how far an object has come or how much weight it carries relative to its size.
The law of cosines, which connects a triangle's sides and angles, can be used to calculate the size of the resulting force:
A2 + B2 - 2ab*cos = C2 (C)
We can define the 8.6 newtons in this case as side a, the 3.5 newtons as side b, and the angle between them as C:
a = 8.6 N b = 3.5 N
C = 58°
By applying the law of cosines, we may determine the length of the resultant force or side c.
c = sqrt(105.36)
c ≈ 10.3
Hence, the force that results has a magnitude of about 10.3 newtons (rounded to the nearest 10th of a newton).
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Find the area of the circle to the nearest hundredths ( Use 3.14 for pi) (4cm)
Answers
Answer: 50.24 cm²
Step-by-step explanation:
ASSUMING THE RADIUS OF THE CIRCLE IS THE 4 CM
The formula for the area of a circle is pi(3.14) * r(4)^2
\(3.14*4^2\)
\(3.14*16\)
\(50.24\)
Hope it helps <3 :D
Standing in your tree house, 50 feet off the ground, you look down at a 60° angle and notice a Frisbee. Approximately how many feet from the base of the tree is the Frisbee? Draw a picture to help you!
Answers
Answer:
About 29 feet.
Step-by-step explanation:
tan 60 = 50 / h
h = 50/ tan 60
= 28.87 ft
a function of x consists of following ordered pais of them form (x, y). Four of the ordered pairs are shown below:
(-2, 7), (0, 3), (1, -4), (5,-2).
Which could be the 5th ordered pair if it were to remain a function?
Answers
Answer:
C
Step-by-step explanation:
It has to be C because other wise an x value would be repeated. If an x value is repeated it is a relation not a function.
Five times the greater of two consecutive even
integers is 14 greater than three times the lesser
number. What is the greater number?
Answers
X, x + 2
5(x+2) = 14 + 3x
5x + 10 = 14 + 3x
2x = 4
X = 2
Greatest is 4
Find how much water can the vase hold
Answers
Step-by-step explanation:
Find endcap area (TWO triangles) = TWO * 1/2 * 2 x3
multiply by height 10
Volume = 2 * ( 1/2 * 2 * 3) * 10 = 60 in^3
How do I solve 3(x−9)=30
Answers
Answer:
x = 19
Step-by-step explanation:
use the distributive property
3(x - 9) = 30
3x - 27 = 30
+27 +27
3x = 57
divide by 3
x = 19
Hope this helped! Have a nice day! Plz mark as brainliest!!! :D
-XxDeathshotxX
Answer:
The value of x is 19.
Step-by-step explanation:
The steps are :
3(x- 9) = 30
3(x - 9) ÷ 3 = 30 ÷ 3 [eliminate 3 on left side]
x - 9 = 10
x - 9 + 9 = 10 + 9 [eliminate -9 on left side]
x = 19
f(n) = 4n +3
g(n) = 3n²+2
Find f(n) - g(n)
help lol
Answers
Answer:
\((4n + 3) - (3 {n}^{2} + 2) \\ = 4n + 3 - 3 {n}^{2} - 2 \\ = - 3 {n }^{2} + 4n + 1 \\ ( - 3 {n}^{2} - 3n) - (1n + 1) \\ - 3n(n + 1) - 1(n + 1) \\ (n + 1)( - 3n - 1) \\ n = - 1 \\ n= \frac{1}{ - 3} \)
Answer:
\(f(n) - g(n) = (4n + 3) - (3 {n}^{2} + 2) \\ = 4n + 3 - 3 {n}^{2} - 2 \\ = \boxed{4n - 3 {n}^{2} + 1}\)
(4n²-3n+1) is the right answer.PLEASE HELP< I WILL GIVE YOU BRAINIEST
What are the real and imaginary parts of the complex number?
−6−i
Answers
Imaginary part: -i
Written as the product of its prime factors, 2250=2x3²x5³. Two integers, A and B, can be written as products of prime factors. A=2xpxq¹ B=2xp² xq² The lowest common multiple (LCM) of A and B is 2250. Write down the values of p, q and r.
Answers
The values of p, q, and r are p = 2, q = 5, and r = 3, respectively.
Given that the lowest common multiple (LCM) of A and B is 2250, and the prime factorization of A is A = 2 × p × q¹, and the prime factorization of B is B = 2 × p² × q², we can compare the prime factorizations to determine the values of p, q, and r.
From the prime factorization of 2250 (2 × 3² × 5³), we can observe the following:
The prime factor 2 appears in both A and B.
The prime factor 3 appears in A.
The prime factor 5 appears in A.
Comparing this with the prime factorizations of A and B, we can deduce the following:
The prime factor p appears in both A and B, as it is present in the common factors 2 × p.
The prime factor q appears in both A and B, as it is present in the common factors q¹ × q² = q³.
From the above analysis, we can conclude:
p = 2
q = 5
r = 3.
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the sum of the measures of the angles in the triangle is 180 degrees. what is the measure of each angle? write and solve an equation
Answers
If sum of the measures of the angles in the triangle is 180 degrees then
measures of each angle is 60 degrees.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given,
The sum of the measures of the angles in the triangle is 180 degrees
By angle sum property, sum of the measures of the angles in the triangle is 180 degrees
Let the measure of angle be x
x+x+x= 180 degrees
3x=180
Divide both sides by 3
x=180/3
x=60
Hence each angle measures 60 degrees.
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can someone help me with this
Answers
Answer:
RQ
Step-by-step explanation:
Since there are congruent, they are mirrored.