Taking the given data into consideration we conclude that the eigenvalues of A are -1 and -4, under the condition that A = [-1 -4 3 -1].
To evaluate the eigenvalues of A = [-1 -4 3 -1], we need to reduce a system of equations with a coefficient matrix of
[tex]A - L_I,[/tex]
Here,
L = scalar and I is the identity matrix. The eigenvalues are the values of L that satisfy the equation
[tex]det(A - L_I) = 0.[/tex]
Firstly , we need to subtract LI from A, where I is the 4x4 identity matrix:
[tex]A - L_I = [-1 -4 3 -1] - L[1 0 0 0; 0 1 0 0; 0 0 1 0; 0 0 0 1][/tex]
[tex]A - L_I = [-1 -4 3 -1] - [L 0 0 0; 0 L 0 0; 0 0 L 0; 0 0 0 L][/tex]
[tex]A - L_I = [-1-L -4 3 -1; 0 -4-L 0 0; 0 0 3-L 0; 0 0 0 -1-L][/tex]
Next, we need to find the determinant of
[tex]A - L_I:det(A - L_I) = (-1-L) * (-1-L) * (-4-L) * (-1-L)[/tex]
[tex]det(A - L_I) = -(L+1)^2 * (L+4)[/tex]
Finally, we need to solve the equation
[tex]det(A - L_I) = 0 for L:-(L+1)^2 * (L+4) = 0[/tex]
This equation has two solutions: L = -1 and L = -4.
Therefore, the eigenvalues of A are -1 and -4.
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The augmented matrix of a system of linear equations AX = B was reduced to upper-triangular form so that 2 1 02 [AB] 3 0 where m and n are real numbers. State all values of m and/or n such that the following statements are true. (a) Matrix A is invertible. (b) The system AX- B has no solutions. (c) The system AX = B has an infinite number of solutions. (a) Columns of the augmented matrix (AB) are linearly independent. (e) The system AX = 0 has a unique solution. (f) At least one eigenvalue of the matrix A is zero. (g) Columns of the matrix A form a basis in R3.
a. Matrix A is invertible when |A| = -m ≠ 0 then statement true.
b. The system AX = B has no solution when m = 0 and n ≠ 0 has a real number then statement true.
c. The system AX = B has an infinite number of solutions when m = n = 0 then statement true.
d. Columns of the augmented matrix (AB) are linearly independent when m ≠ 0 and n= 0 then statement true.
e. The system AX = 0 has a unique solution when m ≠ 0 then statement true.
f. At least one eigenvalue of the matrix A is zero when m = 0 then statement true.
g. Columns of the matrix A form a basis in R³ when m ≠ 0 then statement true.
Given that,
The augmented matrix of a system of linear equations AX = B was reduced to upper-triangular form so that
[A|B] = [tex]\left[\begin{array}{ccc}2&1&0 \ | \ 2\\0&-1&3 \ | \ 1 \\0&0&m \ | \ n\end{array}\right][/tex]
Where m and n are real numbers.
We know that,
a. We have to prove matrix A is invertible.
For A to be invertible.
|A| ≠ 0
|A| is the determinant of the matrix A.
|A| = 2(-m) -1(0) + 0(0) = -m
Here, m is the real number.
So, |A| = -m ≠ 0
Therefore, Matrix A is invertible when |A| = -m ≠ 0 then statement true.
b. We have to prove the system AX = B has no solution.
When Rank[A|B] > Rank[A]
m = 0 and n ≠ 0 has a real number
Therefore, The system AX = B has no solution when m = 0 and n ≠ 0 has a real number then statement true.
c. We have to prove the system AX = B has an infinite number of solutions.
When m = n = 0, and Rank[A] < 3
Therefore, The system AX = B has an infinite number of solutions when m = n = 0 then statement true.
d. We have to prove columns of the augmented matrix (AB) are linearly independent.
When m ≠ 0 and m∈R and n= 0
Therefore, Columns of the augmented matrix (AB) are linearly independent when m ≠ 0 and n= 0 then statement true.
e. We have to prove the system AX = 0 has a unique solution.
When [tex]\left[\begin{array}{ccc}2&1&0 \\0&-1&3 \\0&0&m \end{array}\right]\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}0\\0\\0\end{array}\right][/tex]
The equation are 2x + y = 0, -y + 3z = 0 and mz = 0
m ≠ 0 should be any real number except zero.
Therefore, The system AX = 0 has a unique solution when m ≠ 0 then statement true.
f. We have to prove at least one eigenvalue of the matrix A is zero.
When λ = 2, 1, m
m = 0 then eigen value is zero
Therefore, At least one eigenvalue of the matrix A is zero when m = 0 then statement true.
g. We have to prove columns of the matrix A form a basis in R³.
When m ≠ 0
Therefore, Columns of the matrix A form a basis in R³ when m ≠ 0 then statement true.
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If m(x) = x+5/x-1 and n(x)=x-3, which function has the same domain as (m o n)(x)?
it's simple it's really easy so the answer is 2.0 1682
In a normal distribution, approximately what percentage of scores fall between the z scores of -1.00 and + 1.00?
In a normal distribution, approximately 68% of scores fall between the z-scores of -1.00 and +1.00.
In a standard normal distribution, which has a mean of 0 and a standard deviation of 1, the Empirical Rule (also known as the 68-95-99.7 Rule) applies. According to this rule, approximately 68% of the data falls within one standard deviation from the mean.
Since the z-scores represent the number of standard deviations a particular value is away from the mean, a z-score of -1.00 represents one standard deviation below the mean, and a z-score of +1.00 represents one standard deviation above the mean. Therefore, using the Empirical Rule, we can conclude that approximately 68% of scores fall between these two z-scores (-1.00 and +1.00).
This percentage represents the central portion of the distribution that is within one standard deviation from the mean, providing a useful measure of the spread and concentration of data in a normal distribution.
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find the lateral surface area help needed asap will give brainliest
Step-by-step explanation:
3 Area of lateral = 3 ( bh ) = 12.2 XIO +7.04X12.2 +7.04x 12.2 = 122+85.888+85.888 = 293.776
293.776 approximate to 288
[tex] \frac{ - 48 + 6}{ - 7} + ( - 3)( - 4)( - 2)[/tex]
Step-by-step explanation:
[tex] \frac{ - 48 + 6}{ - 7} + ( - 3)( - 4)( - 2) \\ = \frac{ - 42}{ - 7} + 12( - 2) \\ = 6 + ( - 24) \\ = 6 - 24 \\ = - 18[/tex]
A child toy is made by removing a triangular prism from the center of a wooden rectangular prism The triangular base of the triangular prism has a base length of 1 inch and a height of 1 inch. Write and solve an equation to find the volume of the toy.
*see attachment for the diagram given
Answer:
Volume of the toy = 68 in.³
Step-by-step explanation:
The equation to find the volume of the toy = volume of the wooden rectangular prism - volume of the triangular prism removed form the center
Volume of the toy = (L*W*H) - (½*bhl)
Where,
L = 8 inches
W = 3 inches
H = 3 inches
b = 1 inch
h = 1 inch
l = 8 inches
Plug in the values into the equation
Volume of the toy = (8*3*3) - (½*1*1*8)
Volume = 72 - 4
Volume of the toy = 68 in.³
Jonah has two small bags of assorted doughnuts. Each bag contains exactly 8 powdered doughnuts.
Bag 1 contains 20 total doughnuts.
Bag 2 contains 24 total doughnuts.
What is the probability of Jonah grabbing
a powdered doughnut from
Bag 1?
Answer:
There is a 40% probability of Jonah grabbing a powdered doughnut from Bag 1.
Step-by-step explanation:
Total number of doughnuts in the bag 1 =20
Total powdered doughnuts in each bag = 8
Probability of selecting powdered doughnut from Bag 1 by Jonah =
[tex]\frac{8}{20} * 100\\40[/tex]%
Solve for x.
PLEASE ANSWER I WILL GIVE BRAINLIEST!!
Answer:
16 + 5 =21 21 is your answer
Step-by-step explanation:
Combine the like terms to create an equivalent expression for −n+(−4)−(−4n)+6
Answer:
3n + 2
Step-by-step explanation:
−n+(−4)−(−4n)+6
-n - 4 + 4n + 6
3n + 2
What is 5x÷6=20
Pls help I can't figure it out
Answer:
x= 24
Step-by-step explanation:
5x=20*6
x=120/5
x=24
Hope this helps! Plz mark as brainliest! :)
Make up any linear equation with two variables the solution to which will be these pairs of numbers. x=2, y=4.5 PLS HELP
Answer:
[tex]y = 0.25x + 4[/tex]
[tex](x,y) = (2,4.5)[/tex]
Step-by-step explanation:
Given
[tex]x = 2[/tex]
[tex]y = 4.5[/tex]
Required
Make up a linear function
A linear function is represented as:
[tex]y = mx + b[/tex]
Assume [tex]b = 4[/tex]
The equation becomes
[tex]y = mx + 4[/tex]
Substitute [tex]x = 2[/tex] and [tex]y = 4.5[/tex] to solve for m
[tex]4.5 = m*2 + 4[/tex]
[tex]4.5 = 2m + 4\\[/tex]
Solve for m
[tex]2m = 4.5 - 4[/tex]
[tex]2m = 0.5[/tex]
[tex]m = 0.5/2[/tex]
[tex]m = 0.25[/tex]
So, we have:
[tex]m = 0.25[/tex], [tex]b = 4[/tex], [tex]x = 2[/tex] and [tex]y = 4.5[/tex]
[tex]y = mx + b[/tex] becomes
[tex]y = 0.25x + 4[/tex]
[tex](x,y) = (2,4.5)[/tex]
plllleeeasssw help scams are reporteddd
Least:
Greatest:.
Median
Lower Quartile Range:
Upper Quartile Range:
thx :)
Answer:
Below :)
Step-by-step explanation:
Least/Minimum: 0
Greatest/Maximum: 6
Median: 2
Lower Quartile Range: 1
Upper Quartile Range: 3
Find median:
0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 6
Find Lower Quartile:
0, 1, 1, 1, 1, 1, 1, 2, 2, 2
Find Upper Quartile:
2, 2, 3, 3, 3, 3, 4, 4, 4, 6
In the above figure, m∠AOC = 30° and m∠BOD = (2x + 39)°. If ∠AOC and ∠BOD are vertical angles, what is the value of x? A. x = 69 B. x = -9 C. x = 34.5 D. x = -4.5
i need help asap
Answer:
bestie thats hard
Step-by-step explanation:
Answer:
D. x=-4.5
Step-by-step explanation:
Since they are both vertical angles, m∠BOD must also be equal to 30 degrees, and if you input -4.5 as x, (2 x -4.5x) + 39, that is rewritten as -9 and 39. 39 - 9 is 30 degrees.
which would result in an integer
Answer:
c I think but I am not sure but I hope you have a good day
If an apple pie recipe calls for 3 pounds of candy apples then how many cups of canned apples required
Answer:
Seven cups of canned apples are required to make apple pie recipe
Step-by-step explanation:
The weight of one canned apple is 0.45 pounds
Weight of total canned apple required to make the apple pie recipe is 3 pounds.
Total number of cups of canned apples required
[tex]= \frac{3}{0.45} \\= \frac{300}{45} \\= \frac{20}{3} \\[/tex]
So approximately seven cups of canned apples are required to make apple pie recipe
Correct Given the sample data, find the mean (round to 2 decimals): 23, 27, 35, 44 1.00 points out of 1.00 Flag question Answer: 32.25 Check Correct Marks for this submission: 1.00/1.00 Question 6 Incorrect 0.00 points out of 1.00 Given the data from problem 5 (sample data: 23, 27, 35, 44), find the sum of the squared deviations (the numerator of the fraction under the square root in the formula). In finding the number, round all calculations to 2 decimals (if you carry more or fewer your answer may be off enough to be marked incorrect on this system).
The sum of the squared deviation for the given sample data (23, 27, 35, 44) is 212.00.
In statistics, the squared deviation is calculated by subtracting each data point from the mean and then squaring the result. The sum of these squared differences gives us a measure of how much the individual data points vary from the mean.
Find the sum of squared deviations, we first calculate the mean of the data set. In this case, the mean is found by adding up all the values (23 + 27 + 35 + 44) and dividing the sum by the number of data points (4).
The mean turns out to be 32.25.Next, we subtract the mean from each data point:
(23 - 32.25) = -9.25
(27 - 32.25) = -5.25
(35 - 32.25) = 2.75
(44 - 32.25) = 11.75
Then, we square each of these differences:
(-9.25)² = 85.56
(-5.25)² = 27.56
(2.75)² = 7.56
(11.75)² = 138.06
Finally, we sum up these squared deviations:
85.56 + 27.56 + 7.56 + 138.06
= 212.00
Therefore, the sum of the squared deviations is 212.00 (rounded to two decimal places).
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12 × (3 + 2²) ÷ 2 - 10
Answer:
32
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
This should help
PLEASE HELP
WILL GIVE BRAINLIEST
Identify the situation that each graph could represent.
A ray is graphed in the first quadrant. The horizontal axis is labeled Time. The ray starts at the bottom left and continues to the upper right.
A. the length of a necklace that you make at a rate of 10 cm per hour without taking a break
B. the height of a balloon as it rises, gets caught in a tree for a few minutes, and then continues to rise
C. the total distance you are from home if you ride your bicycle three miles per hour for one hour, and then stop and take a rest
D. The volume of water in a bath tub as it is draining.
Answer:
The answer your looking for is, C.
It's been found that there is a 15% chance (3 out of 20) that you can
win a particular game. How many "wins” would you have if you
played 80 times?
Consider the inequality x<1. Determine whether each value of x makes the inequality trueSelect Yes or No va Yes No 3/2 13/6
Which of the following sets of ordered pairs does not define a function?
{(1,2),(5,6),(6,7),(10,11),(13,14)}
{(−1,4),(0,4),(1,4),(2,4),(3,4)}
{(1,1),(2,2),(3,3),(4,4),(5,5)}
{(1,3),(5,2),(6,9),(1,12),(10,2)}
Answer: D
Step-by-step explanation: As we can see, D is the only one that has matching inputs, but those inputs have separate outputs. If they don't have the same output, it is not a function
Hope this helps :)
Convert the point from Cartesian to polar coordinates. Write your answer in radians. Round to the nearest hundredth.
(−10,1)
The point (-10, 1) in Cartesian-Coordinates can be represented in polar coordinates as approximately (10.05, 3.0416 radians).
To convert the point (-10, 1) from Cartesian-Coordinates to polar coordinates, we can use the formulas:
r = √(x² + y²)
θ = arctan(y / x)
We know that, the point is (-10, 1), we substitute the values into the formulas:
We get,
r = √((-10)² + 1²) = √(100 + 1) = √101 ≈ 10.05, and
The point lies in second-quadrant, so, the angle is measured counterclockwise from the positive x-axis, which means it is between π/2 and π radians.
Therefore, The adjusted θ is : θ = π + arctan(1/-10) ≈ 3.0416 radians.
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What is the equation of the line that passes through the point (7,-6) and has a slope of -2?
Answer:
y=-2+8
Step-by-step explanation:
The answer is y=-2+8 because of course the slope has to be -2 as you stated in your Question. So all you have to do is change the Y-Intercept until you reach the point. Since the Slope is negative, the Y-Intercept will rise until you reach your point. You may double check my answer to see if it is right, it is up to you. If you find any fault in my answer please let me know. Have a good day!
Find the length of the diagonal of
rectangle whose length
is 12ft and whose
width 5 ft
Answer:
13 ft
Step-by-step explanation:
The formula to find the length of the diagonal of a rectangle =
Diagonal² = Length² + Width²
Diagonal = √Length² + Width²
Length = 12 ft
Width = 5ft
Diagonal = √12² + 5²
Diagonal = √144 + 25
Diagonal = √169
Diagonal = 13 ft
The length of the diagonal of the rectangle = 13 ft
A structural steel rod 1-1/2 in. in diameter and 20 ft long supports a balcony and is subjected to an axial tensile load of 30,000 lb. Compute: (a) the total elongation (b) the diameter of the rod required if the total elongation must not exceed 0.10 in. A. a. Elongation = 0.2358in. b. Use a1-1/2" dia. Rod B. a. Elongation = 1.1358in. b. Use a 1-1/4" dia. Rod C. a. Elongation = 0.1358in. b. Use a 1-3/4" dia. Rod D. a. Elongation = 0.1458in. b. Use a 3/4" dia. Rod
The diameter of the rod required to limit the total elongation to 0.10 inches is approximately 1-1/2 inches (or 1.441 inches to be more precise). Hence, the correct answer is option (A) with an elongation of 0.2358 inches and using a 1-1/2" diameter rod.
(a) To compute the total elongation, we can use the formula:
Elongation = (P * L) / (A * E)
where P is the axial tensile load, L is the length of the rod, A is the cross-sectional area of the rod, and E is the modulus of elasticity for the material.
Given:
P = 30,000 lb
L = 20 ft = 240 in
Diameter of the rod = 1-1/2 in
First, we need to calculate the cross-sectional area:
Area = π * (diameter/2)^2
Area = π * (1.5/2)^2
Area ≈ 1.767 in^2
Next, we need to determine the modulus of elasticity for the material. Assuming it's a standard structural steel, we can use a typical value of 29,000,000 psi.
Now we can plug the values into the formula:
Elongation = (30,000 * 240) / (1.767 * 29,000,000)
Elongation ≈ 0.2358 in
Therefore, the total elongation is approximately 0.2358 inches.
(b) If the total elongation must not exceed 0.10 inches, we need to determine the diameter of the rod that satisfies this requirement.
We can rearrange the formula for elongation to solve for the cross-sectional area:
A = (P * L) / (E * Elongation)
Using the given values:
A = (30,000 * 240) / (29,000,000 * 0.10)
A ≈ 2.069 in^2
To find the corresponding diameter, we use the formula:
Diameter = √(4 * A / π)
Diameter = √(4 * 2.069 / π)
Diameter ≈ 1.441 in
Therefore, the diameter of the rod required to limit the total elongation to 0.10 inches is approximately 1-1/2 inches (or 1.441 inches to be more precise). Hence, the correct answer is option (A) with an elongation of 0.2358 inches and using a 1-1/2" diameter rod.
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what differences can be found when contrasting the mood of third person acc with that of claudettes first person account?
Answer: The mood of the third-person account is less emotional and more matter-of-fact. The mood of Claudette's account is less emotional and more matter-of-fact.
Step-by-step explanation:
PLEASE HELP:
The distance d, in kilometers, that a car travels at a speed of 80 km per hour, for t hours, is given by the equation d= 80t. What is the inverse to represent time, t as a function of distance, d?
Choices:
1. t= d/80
2.t= 80/d
3.t= 80d
Answer:
The car was traveling for 1.5 hours.
Step-by-step explanation:
Given that distance d, in kilometers, that a car travels at a speed of 80 km per hour , for t hours, is given by the equation d=80t.
Here wee need to find the time if the car has gone 120 kilometers.
That is
d = 120 km
we need to find t.
d=80t
120 = 80 x t
The car was traveling for 1.5 hours.
Mr. Frederick teaches 4 math classes. Which class period has the most students? Use the bar graph to answer the question.
Answer:
The class in the second and longest bar graph (the one labeled 3) has the most students.
Step-by-step explanation:
When looking for the largest amount of something in bar graphs, the largest bar graph is correct. In this case the second bar graph is the longest, and we can see it indicates the class contains 28 students.
Solve for x.
20
8
4x+3
38
Answer:
x = 18
Step-by-step explanation:
The "Angle Bisector" Theorem says that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle.
So, 20/8 = (4x + 3)/30
8(4x + 3) = 20(30)
32x + 24 = 600
32x = 576
x = 18