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-
Answers
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 \([I|A^{(-1)]\).
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\([I|A^{(-1)]\), where \(A^{(-1)\) 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] \(\times\) \(A^{(-1)\) = [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 \(A^{(-1)\) and the solution set, the calculations need to be performed manually using the given coefficients of the equations.
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Related Questions
f(x) = x + 2 and g(x) = x2 – 4
What is (fºg)(x)?
x² –2
x² + 4x
x² + 4x-2
Answers
Answer:
x^2-2
Step-by-step explanation:
Sorry I dont have an explanation, its saying its saying its not valid and I am in a rush rn.
Answer:
for the first box its: x²-2
for the second box its: 2
for the third box its: B
for the fourth box its: 12
Step-by-step explanation:
i just did the assignment on edge
Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?
Answers
Chay can use 3 bags of mulch per flower bed.
Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?The number of bags of mulch that can be used in each flower bed can be found by dividing the total number of bags of mulch by the number of flower beds, as given by the problem.Let X be the number of bags of mulch used in each flower bed. Then, the following equation can be written:Total number of bags of mulch = X × number of flower beds (20)Or, 55 = 20XDividing both sides of the equation by 20, we get: X = 55/20X = 2.75.Therefore, Chay can use 2.75 bags of mulch in each flower bed. However, since we cannot have a fraction of a bag of mulch, she would have to round up to 3 bags of mulch per flower bed to ensure each flower bed has enough mulch.
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The average low temperatures in international falls minnesota are shown in the graph f(x) represents the function that contains these points find each of the following
Answers
The Relative Maximum will be (7, 50) and minimum is (12, 0).
We have the graph showing average low temperatures in international falls minnesota.
From the graph the maximum y coordinate is 50.
So, the Relative Maximum will be (7, 50).
and, the minimum y coordinate is 0.
So, the Relative minimum is (12, 0)
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The mean life of a television set is 138 months with a variance of 324. If a sample of 83 televisions is randomly selected, what is the probability that the sample mean would be less than 143.4 months
Answers
Answer: 0.9968
Step-by-step explanation:
Let \(\overline{X}\) be the sample mean life of television.
Given: \(\mu=138,\ \ \ \sigma^2=324\Rightarrow\ \sigma=\sqrt{324}=18,\ \ \ , n=83\)
The probability that the sample mean would be less than 143.4 months will be :
\(P(\overline{X}<143.4)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{143.4-138}{\dfrac{18}{\sqrt{83}}})\\\\=P(Z<2.733)=0.9969\ \ \ [\text{By p-value table}]\)
hence, the required probability = 0.9968
You can use the notation P(A), read “the probability of event B, given event A” to write a
A. Probability distribution
B. Frequency table
C. Conditional probability
D. Cumulative probability
Answers
You can use the notation P(A), read “the probability of event B, given event A” to write a conditional probability. The correct answer is C.
Conditional probability refers to the probability of one event occurring given that another event has already occurred. In this case, we are interested in the probability of event B occurring given that event A has already occurred, and we can represent this using the notation P(B|A), where '|' means 'given'.
For example, let's say we are interested in the probability of getting a head on a coin toss (event B), given that the coin was flipped and landed on heads (event A). We could represent this using the notation P(B|A). The value of P(B|A) would be 1, because if the coin already landed on heads, then the probability of getting a head on the next flip is certain.
Conditional probability is an important concept in probability theory and is often used in real-world applications, such as predicting the likelihood of a disease given certain symptoms, or the probability of an event occurring given certain conditions.
The correct answer is C.
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A wooden artifact is found in an ancient tomb. Its carbon-14 14 6 C activity is measured to be 65.0% of that in a fresh sample of wood from the same region. Assuming the same amount of 14C was initially present in the artifact as is now contained in the fresh sample, determine the age of the artifact.
Answers
Answer:
3560.622 yr
Step-by-step explanation:
See the attachment for calculation details
Find a possible equation of a rational function for the graph.
Answers
A possible equation of a rational function for the graph could be:f(x) = (x-2)/(x-1)²
What is equation?An equation is a mathematical statement that uses an equal sign to describe the relationship between two or more components or variables. It is a way of expressing a condition or a scenario through mathematical terms and symbols. Equations are used to solve problems in a variety of fields, such as physics, chemistry, engineering, economics, and mathematics. In general, an equation has two sides: the left side and the right side, each of which contains numbers and/or variables. The left side is equal to the right side, so if some of the values or variables are known, the unknown values or variables can be determined.
This equation would represent a graph that has a vertical asymptote at x = 1, a hole at x = 2, and an x-intercept of 2. The graph would also have a slant asymptote at y = 1. The graph would also be continuous for all x-values except for x = 1.
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who ever gets it correctly gets 100 points
Answers
1/10 × 2000
1×2000/10
2000/10
200
Write this number in standard form 3 thousands, 16 tens,7 ones
Answers
Evaluate the expression when:
a = 6, b = 2, and c = 4
3a + 40 - 6b
Answers
Answer:
46
Step-by-step explanation:
3(6)+40-6(2)
18+40-12
58-12
46
Find the value of: i) (4/3)³ x (3/5)-² (2/5)-²
Answers
Answer:
Step-by-step explanation: 10000/243
In a triangle with angles measuring a, b and c degrees, the mean of b and c is a. What is the
value of a?
Answers
Answer:
60
Step-by-step explanation:
\(a+b+c=180\\\frac{b+c}{2}=a \rightarrow b+c=2a\\\\a+2a=180\\3a=180\\a=60\)
Therefore, the value of a is 60 degrees
help me find the slope please
Answers
Answer:
3/4
Step-by-step explanation:
Ok, so I see that the x-intercept is (4,0), while the y-intercept is(-3,0)
Slope is rise/run
Between these two points, the line rose 3 and horizontally went 4 units to the right. Therefore, the slope is 3/4.
Feel free to tell me if I did anything wrong! :)
Also, if you're still confused, I could explain it another way.
Little help ?please 5 points
Tawna and Donnie Milled cartons with bottles, Tawna put in 10 bottles and Bonnie put in a bottles, How many bottles does each carton hold?
Answers
Answer:
I Think E But Im Not Sure About It
27,813 students took the ACET this year. If only 2,836 students were admitted into the Ateneo among those students, what is the Ateneo’s acceptance rate? a. 7.5% b. 10.2% c. 13.4% d. 9.0%
Answers
If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.
How the rate is determined:The rate is the ratio of one value, expression, measurement, or quantity compared to another.
The rate represents the quotient of the numerator and the denominator.
The rate is expressed as a percentage by multiplication with 100.
The number of students who took the ACET this year = 27,813
The number of students who were admitted into the Ateneo = 2,836
The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)
= 10.2%
Thus, we can conclude that the acceptance rate or percentage is Option B.
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select the correct answer which graph is defined by f(x)= |x^2 -x-2|
Answers
The graph of the absolute value function can be seen below.
How to get the graph of f(x)?Here we have the absolute value function:
\(f(x) = |x^2 - x -2|\)
Notice that the argument of the absolute value function is a quadratic equation, then the graph of the function f(x) will be the graph of the quadratic equation, but such that the part below the horizontal axis is reflected.
Then the graph of the function is the one you can see below:
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The following information matrices shows how many of each Video Game Consoles that each
electronics store sold during one weekend and the price that is charged for each gaming console at all
3 stores.
Answers
Micro middle sold the least no of different types of consoles.
What are matrices?Matrices represent data in the form of rows and columns together as an array form.
From matrix A we get the data as follows,
A row represents shops and columns represents types of console.
Games Go sold (53 + 21 + 48) = 122 different types of consoles.
Better Buy sold (65 + 34 + 70) = 169 different types of consoles.
Micro middle sold (18 + 11 + 15) = 34 different types of consoles.
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Type < or > to make this statement true
Answers
Answer:
- \(\frac{9}{10}\) > - \(\frac{10}{10}\)
Step-by-step explanation:
Which number is closer to 0, meaning that number is bigger.
-9/10 = -0.9
-10/10 = -1
We see -0.9 is closer to 0, meaning it is bigger.
So, - \(\frac{9}{10}\) > - \(\frac{10}{10}\)
You can use the equation A =(HW/3600)^1/2
to approximate a person's body surface area A (in square meters), where H
is height (in centimeters) and W is weight (in kilograms). Approximate the body surface area of a person with a height
of 160 centimeters and a weight of 64 kilograms.
Body surface area:______
m²
Answers
The body surface area is given by the equation A = 1.6865 m²
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the body surface area be represented as A
Now , the equation will be
A = ( HW / 3600 )^1/2
A = √( HW / 3600 ) be equation (1)
where H is the height in centimeters and W is the weight in kilograms
Now , the value of H = 160 cm
The value of W = 64 kg
Substituting the values in the equation , we get
A = √ [ ( 160 x 64 ) / 3600 ]
On simplifying the equation , we get
A = √ ( 10240/3600 )
A = √ ( 2.8444 )
A = 1.6865 m²
Therefore , the body surface area is 1.6865 m²
Hence , the equation is A = 1.6865 m²
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What is the perimeter of Quadrilateral ABCDwith vertices at A(−11, −6), B(−3, 0), C(1, 0), and D(1, −6)?
Answers
Answer:
32 units
Step-by-step explanation:
the perimeter =
(1 -(-3)) +(0-(-6)) + (1 -(-11) + (√(12-4)²+6²)
= (1+3) +(0+6) +(1+11) +(√(64+36))
= 4+6+12 + 10
=32 units
5(2x+1)=3(x+4)-5. What is x
Answers
Answer:
x = 2/7
Step-by-step explanation:
isolate the variable by dividing each side by factors that don't contain the variable
A triangular prism and its dimensions are shown in the diagram. What is the lateral surface area of this triangular prism in square feet?
Answers
Answer:
112 ft
Step-by-step explanation:
AL = (a+b+c)h
= (6+12+10) x 4
= 112 ft
Find the area of the shaded region.
Answers
Answer:
49.72ft^2
Step-by-step explanation:
(4x14)-(1/2 x pi x 2^2)
56-(1/2 x pi x 4)
56-2pi
Taking Pi at 3.14....
56-6.28=49.72ft^2
You want to buy a $ 16,249 car. The company is offering a 3.7 % interest rate for 61 months . What will your monthly payments be?$__________ (Round to 2 decimal places if necessary)
Answers
Hello! To solve this exercise, we have to use the formula below:
Compound Interest:
\(A=P(1+\frac{r}{100})^t\)Let's replace with the values:
\(undefined\)the angle of elevation from the bottom of the lift to the top of Snowbowl mountain is 33 degrees. If the height of the mountain is 544 meters, what is the length of a list from the bottom of a mountain to the top?
Answers
Answer:
Step-by-step explanation:
\(tan33=544/x\\ \\ x=\frac{544}{tan33}m\\ \\ x\approx 837.7m\)
9514 1404 393
Answer:
999 meters
Step-by-step explanation:
The length of the lift line represents the hypotenuse of a right triangle. The side opposite the given angle is the height of the mountain. The applicable trig relation is ...
Sin = Opposite/Hypotenuse
We want to find the hypotenuse, so we use the rearranged form ...
hypotenuse = (mountain height)/sin(33°)
lift length = (544 m)/sin(33°) ≈ 998.83 m
The length of the lift from bottom to top is about 999 meters.
Find LCM of 18,24,56
Answers
Answer: 504
Step-by-step explanation:
Least Common Multiple is :
504
Calculate Least Common Multiple for :
18, 24 and 56
Factorize of the above numbers :
18 = 2 • 32
24 = 23 • 3
56 = 23 • 7
Build a prime factors table
Number of times each prime factor
appears in the factorization of :
Prime
Factor Number
18 Number
24 Number
56 L.C.M
(max)
2 1 3 3 3
3 2 1 0 2
7 0 0 1 1
LCM = 23 • 32 • 7
Least Common Multiple is :
504
A company produced in the first quarter 6,905 pieces in the second quarter the same company produced 795 pieces more than in the first quarter under these conditions how many pieces did the company produce in the first semester?
Answers
Answer: 14,605 pieces.
Step-by-step explanation:
In the second quarter, the company produced 795 pieces more than in the first quarter.
So, the total pieces produced in the second quarter can be calculated as:
6905 + 795 = 7700
The total pieces produced in the first semester (two quarters) can be calculated as:
6905 + 7700 = 14,605
Therefore, the company produced 14,605 pieces in the first semester.
The number of pieces the company produced in the first semester was 14,605 pieces.
How many?The question asks to calculate how many pieces a company produced in the first semester, considering the production of two quarters.
In the first quarter, the company produced 6,905 pieces, as indicated in the question.
Already in the second quarter, the company produced 795 more pieces than in the first quarter, which means that the production in the second quarter was:
6,905 + 795 = 7,700 pieces.
To know the company's total production in the first semester, just add the productions of the two quarters:
6,905 + 7,700 = 14,605 pieces
x = ??? What is x?? Solve for x
Answers
Answer:
x= 11
Step-by-step explanation:
4x-8 = 3x+3 (those angles are corresponding angles so they are equal to each other)
4x-3x =3+8
x =11
4x - 8 = 3x + 3
We know this since they are corresponding angles.
1X = 8 + 3
8 + 3 = 11 therefore that is the answer.
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Solve the equation and check it. Put in all your steps including check.
8 (4-a)=2a
Answers
Answer:
answer is 3.2
Step-by-step explanation:
Simplifying
8[4 + -1a] = 2a
[4 * 8 + -1a * 8] = 2a
[32 + -8a] = 2a
Solving
32 + -8a = 2a
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-2a' to each side of the equation.
32 + -8a + -2a = 2a + -2a
Combine like terms: -8a + -2a = -10a
32 + -10a = 2a + -2a
Combine like terms: 2a + -2a = 0
32 + -10a = 0
Add '-32' to each side of the equation.
32 + -32 + -10a = 0 + -32
Combine like terms: 32 + -32 = 0
0 + -10a = 0 + -32
-10a = 0 + -32
Combine like terms: 0 + -32 = -32
-10a = -32
Divide each side by '-10'.
a = 3.2
Simplifying
a = 3.2
Answer:
a = 3.2
Step-by-step explanation:
if the linear equation is: 8 (4-a)=2a the value of a would be 3.2 because
a = 16/5 which equals to 3 1/5 which is the same as 3.2
ANSWER THIS WITH EXACT SOLUTION!.
Two ladders are leaning against a wall as shown, making the same angle with the ground. The longer ladder reaches 40 feet up the wall. How far up the wall does the short ladder reach?
Answers
for example, l is the length of short ladder we want to find
Make a comparison
ladder/wall height = ladder/wall height
l/20 = 50/40
l/20 = 5/4
l = 5/4 × 20
l = 100/4
l = 25
The short ladder is 25 ft
Therefore, The short ladder is 25 ft
===================================
\( \large \sf \underline{Problem:}\)
Two ladders are leaning against a wall as shown, making the same angle with the ground. The longer ladder reaches 40 feet up the wall. How far up the wall does the short ladder reach?===================================
\( \large \sf \underline{Answer:}\)
\(\huge \sf \qquad \quad{ 16 \: feet }\)
===================================
\( \large \sf \underline{Solution:}\)
Setting up the equation, establish the best proportion.
\( \large : \implies\qquad\large \sf\dfrac{x}{40} =\large\sf \dfrac{20}{50} \)
Solving the equation, setting up the ratios and then cross multiply.
\( \qquad\large \sf\dfrac{x}{40} = \large \sf \dfrac{20}{50} \)\( \qquad\large \sf{(x)(50 \: ) = } \large \sf {(20)(40)}\)\( \qquad\large \sf{50x \: = 800 }\)\( \qquad\large \sf\dfrac{50x}{50} = \large \sf\dfrac{800}{50} \)\( \qquad\large \sf{ \underline{ \underline{\pmb {x \: = \: 16 }}}}\)Hence, the short ladder reach the wall up to 16 feet.
===================================