Let S denote the vector space of solutions to the differential equation my" - 8«y' + 18y = 0. Circle each set below, if any, that is a basis for S. Show work or explanation to justify your answer: Si = {x} S2 = {x",) S3 = {3.8 +67"} Su = {z + 4x0,728 - } Ss = {x....) b). • Prove that if S-AS = B for some invertible matrix S and v is an eigenvector of A corresponding to then S-lv is an eigenvector of B corresponding to . c) • Let {vi. Va be a linearly independent set of vectors in a vector space V. Prove that if va span{ V1.va). then {V1, V2, V3} is a linearly independent set. d). TRUE or FALSE: If A is a 13 x 4 matrix will nullity(A) 0, then colspace(A) = R'.
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The sets given are not bases for the vector space of solutions to the differential equation. A property of invertible matrices is explained. If a set of vectors is linearly independent and spans a subspace, then adding another vector to the set maintains linear independence. The statement about nullity and column space is false.
a) None of the sets Si, S2, S3, Su, or Ss is a basis for the vector space S of solutions to the given differential equation.
b) Let A be the matrix associated with the linear transformation defined by the differential equation. If S is an invertible matrix such that SAS⁻¹ = B, where B is another matrix, and v is an eigenvector of A corresponding to the eigenvalue λ, then S⁻¹v is an eigenvector of B corresponding to the eigenvalue λ.
c) Suppose {v₁, v₂, v₃} is a linearly independent set of vectors in a vector space V. If va spans the subspace span{v₁, v₂}, then {v₁, v₂, v₃} is also a linearly independent set.
d) FALSE. If A is a 13 x 4 matrix with nullity(A) = 0, it means that the matrix has no nontrivial solutions to the homogeneous system Ax = 0. This implies that the columns of A are linearly independent, but it does not guarantee that colspace(A) = ℝⁿ. The column space of A could still be a proper subspace of ℝⁿ.
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Related Questions
Consider the points below. P(θ),−4,0),Q(5,1,−2),R(6,4,1) (a) Find a nonzero vector orthogonal to the plane through the points P,Q, and R. (b) Find the area of the triangle PQR.
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(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.
(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:
PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)
PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)
Taking the cross product of PQ and PR, we have:
n = PQ x PR = (9, 1, -2) x (10, 4, 1)
Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.
(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:
|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)
Evaluating the magnitude gives |n| = \(\sqrt\)(811).
The area of triangle PQR is then:
Area = |n| / 2 = \(\sqrt\)(811) / 2.
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Line AB and line CD intersect at point E, with point E between A and B and between C and D. Which rays are opposite rays?
Answers
Answer:
EA, EB, EC and ED are opposites rays.
Step-by-step explanation:
Given that,
Line AB and line CD intersect at point E.
According to figure,
We need to find opposite rays
Using diagram
We draw a first line AB and second line CD which is intersect of AB at point E.
Now, EA and EB is called opposite ray of first line AB.
Similarly,
EC and ED is called opposite ray of first line CD.
Hence, EA, EB, EC and ED are opposites rays.
imagine an island that is 1 square mile. the island has a population of 1950 people. although the island is not perfectly square, the image below can help us imagine the situation. 1
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ANSWER:
a. 1950 people per square mile
b. The island's area got smaller
c.
\(\frac{1950\text{ people}}{0.5\text{ square mile}}\)STEP-BY-STEP EXPLANATION:
Population density is the average number of people living per unit area. It is calculated by dividing the total number of population of a geographical unit (in this case it is the island) by the total amount of surface.
a.
Therefore:
\(Density=\frac{1950\text{ people}}{1\text{ square mile}}=1950\text{ people per square miles}\)b.
Since the size of the island is halved without losing any people, we can conclude that the area has become smaller.
Therefore:
The island's area got smaller
c.
Since it is half the area, the new density would be:
\(Density=\frac{1950\text{ people}}{0.5\text{ square mile}}\)Triangle RST is similar to triangle WXY.
Which statement is a proportionality statement for the ratio of the
sides of the triangles?
O
0 0
O
RS = WT
XY
WX
RS
CE CR CE CR
||
RS
WX
ST
YW XY
ST
=
=
=
RS = ST =
WX
TR
YW
TR
WX
TR
XY
TR
YW
R
S
Answers
Answer:
4th option i.e. RS/WX=ST/XY=TR/YW
Answer:
This is for you for your question that you were asking me I had to do it in picture form is this the correct answer?
Step-by-step explanation:
The midpoint M and one endpoint of JK are given. Find the coordinates of the other endpoint. J(7,2) and M(1,-2)
Answers
Step-by-step explanation:
Xj + Xk/2 = Xm
7 + Xk/2 = 1
to get rid of the bracket, multiply all two sides by the denominator.
2(7 + Xk/2) = 1(2)
7 + Xk = 2
Xk = 2 - 7
Xk = -5
Yj + Yk/2 = Ym
2 + Yk/2 = -2
to get rid of the bracket, multiply all two sides by the denominator.
2(2 + Yk/2) = -2(2)
2 + Yk = -4
Yk = -4 - 2
Yk = -6
Therefore the coordinates of point K is (-5,-6)
Please answer the two questions in the photo ( will mark brainliest if correct )
Answers
A rhombus has 2 lines of symmetry and so does the other shape
Kurt has c comic books. Sandra has 18 times as many comic books as Kurt. Write an expression that shows how many comic books Sandra has.
Answers
Answer:Sandra = 18c
Step-by-step explanation:
Given that Kurt has c comic books
And
Sandra has 18 times as many comic books as Kurt.
We can say the expression to show how many comic books Sandra has will be
Kurt = c
Sandra = 18c
line m can be represented by the equation 3x-6y=18. Write an equation of the line perpendicular to line m that passes through the point (-4,1)
Answers
Step-by-step explanation:
the perpendicular line can be represented by bx-ay+k=0 ,So the second step Is Written
since the line passes through point (-4,1) ,the value of x and y is Substitute as written in answer
Answer:
y=-2x-7
Step-by-step explanation:
3x-6y=18 also equals 3x-18=6y
divide both sides by 3 to get x-6=2y or y=x/2-3 as same line then, to find inverse switch x and y, x=(y/2)=3 and solve for y, y-6=2x, -y=2x+6 is the inverse then to make it pass thru (-4,1) change b value, y=-2x-7
A ping-pong ball rolls forward 6 meters, and bounces backward 3 meters. It traveled a total distance of:.
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The distance traveled by the ping-pong ball as it rolls forward 6 meters and bounces backward 3 meters is 3 meters.
Distance is a concept that is important to understand in physics and mathematics. It refers to the amount of space between two points. In this scenario, we will be discussing the distance traveled by a ping-pong ball as it rolls forward and bounces backward.
When the ping-pong ball rolls forward, it covers a distance of 6 meters. This can be represented mathematically as d1 = 6 meters.
When the ball bounces backward, it covers a distance of 3 meters. This can be represented as d2 = -3 meters which means the negative sign indicates that it is moving in the opposite direction.
The total distance traveled by the ball can be found by adding the distance traveled in each direction. This can be represented as
=> d = d1 + d2 = 6 + (-3) = 3 meters.
In other words, the total distance traveled by the ball is 3 meters, which is the net distance covered after taking into account both the forward and backward movements.
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Question:
Taylor tried to solve an equation step by step, Fond Taylor’s mistake
Options:
A-step 1
B-step 2
C-step 3
D- Taylor did not make a mistake
(Picture is step by step equations)
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Answer:
Step 1
Step-by-step explanation:
7 should have been multiplied by 4.5
0
с
z←
85⁰
D
Work out the three-figure bearing of D from C.
Answers
Answer:
095
Step-by-step explanation:
You want the bearing from C to D, given that the bearing from D to C is 85° west of north.
BearingThe bearing from C to D will be the opposite of the bearing from D to C.
Bearing is measured clockwise from north, so the bearing shown from D to C is -85°. Its opposite is found by adding 180°.
180° +(-85°) = 95°
The 3-digit bearing of D from C is 095.
A
Plz help!!!!!! !!!!!!!!!!!
Answers
Answer:
R is at the ordered pair (4, -2)
Step-by-step explanation:
Josiah plants vegetable seeds in rows. Each row has the same number of seeds in it. He plants more than one row of seeds. What could be the total number of seeds he plants?
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The total number of seeds that Josiah would plant would be = nR×S
How to determine the total number of seeds that Josiah will plant?To determine the total number of seeds that Josiah will plant will be to add the seeds in the total number of rooms he planted.
Let each row be represented as = nR
Where n represents the number of rows planted by him.
Let the seed be represented as = S
The total number of seeds he planted = nR×S
Therefore, the total number of seeds that was planted Josiah would be = nR×S.
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Miss Lewis has $523.50 in her savings account. Her bank pay 5 3/4%
interest. If the interest is computed once per year, how much interest will
she make in one year?
Answers
Answer:
30.10125
Step-by-step explanation:
Tell me if you need a step b step explanation
if 12x+8 is less than 6,what is the value of 8x
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Calculate X and leave your answer to 3 significant figures.
Answers
Answer:
x=9.23
Step-by-step explanation:
Zy=x
Yx=11
Tan40=x/11
11tan40=x
11x0.8391
x=9.23
simplify each expression using the order of operations
6 + 4/a + b/3 when a = 4 and b = 3
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10/4 + 3/3 (add 6+4)
5/2 + 1 (Simplify fractions)
2 1/2 + 1 (Write improper fraction as proper fraction)
3 1/2 (add)
Answer: 3 1/2 (three and a half)
Economic growth typically results in rising standards of living and prosperity. However, it also invites negative externalities such as environmental degradation due to over- exploiting of natural resources. As such, the world is confronted with the dilemma of growth versus environmental sustainability. Developing a model explaining the disparity of economic development concentrating on drivers such as tourism sustainability, technological innovation and the quality of leadership would be important not only to facilitate future economic growth in developing countries, but also to the environmental and sociocultural sustainability which ultimately lead to global sustainable development. The present research objective is to develop and test framework of sustainable development by considering the elements of tourism, technological innovation, and national leadership. This further would facilitate growth, environmental and socio-cultural sustainability. Understanding the integration of these dimensions would enable the building of a Sustainable Development Framework (SDF) that would provide better insight in promoting the SDGS agenda. Ultimately, growth and environmental sustainability can be achieved which will benefit the society, the economy, and nations and of course for future sustainable policy recommendation. Based on the issue above, you are required to propose relevant econometric approaches with the aims to test sustainable development by considering the elements of tourism, technological innovation, and national leadership. Question 1 [10 marks] [CLO2] Based on the scenario above, a. Propose an appropriate model specification based on the scenario above. [4 marks] used in the [4 marks] [2 marks] b. Justify the selection of the dependent and independent variables model. c. Justify the selection of the sample period.
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According to the given information, the sample period should be from 2010-2020.
a) Model specification
The model specification based on the scenario above is as follows:
SDF= f(T, TI, NL)
Where: SDF= Sustainable Development Framework
T= Tourism
TI= Technological innovation
NL= National leadership
b) Justification for the selection of the dependent and independent variables model:
Dependent variable: The dependent variable in this model is Sustainable Development Framework (SDF). The model seeks to develop a framework for sustainable development that would facilitate growth, environmental and socio-cultural sustainability.
Independent variables:
The independent variables are tourism sustainability, technological innovation, and quality of leadership. These variables drive economic development. The inclusion of tourism sustainability reflects its importance in the global economy and its potential to drive growth.
The inclusion of technological innovation reflects its potential to enhance productivity and create new industries. The inclusion of national leadership reflects the role of governance in promoting sustainable development and managing negative externalities.
c) Justification for the selection of the sample period:
The sample period should be selected based on the availability of data for the variables of interest. Ideally, the period should be long enough to capture trends and patterns in the data. However, it should not be too long that the data becomes obsolete or no longer relevant.
Additionally, the period should also reflect the context and relevance of the research question. Therefore, the sample period for this study should cover the last decade to capture the trends and patterns in the data and reflect the relevance of the research question.
The sample period should be from 2010-2020.
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What is the answer to this?
Answers
Answer:
\(\huge\boxed{-6}\)
Step-by-step explanation:
Since we know the values of a, b, and c, we can substitute them into our expression and get the value.
\(-2b + | -3c + a |\\\\-2(6) + |-3(-3) + -3 |\)
A negative multiplied by a negative gets us a positive.
\(-2(6) + |9 + -3 |\)
Adding a negative is the same as subtracting a positive.
\(-2(6) + |9 -3 |\\-2(6) + 6\)
\(-2 \cdot 6 = -12\\\\-12+6\\\\-6\)
Hope this helped!
The equations of four lines are given. Identify which lines are perpendicular.
Line 1: y=-5
Line 2: g=12-1
Line 3: r=-6
Line 4: y+5= -4(2+1)
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If g(x) = 2 − 1, what is g(−2.3)?
Answers
What is the value of x?
Answers
between 120 and 97
Step-by-step explanation:
Find the angle between u =(8,-2) and v =(9,3) Round to the nearest tenth of a degree.
A. 32,5
B. 6. 3
c. 42. 5
d. 16. 3
Answers
The angle between vectors u and v is approximately 32.5 degrees. The correct answer is A. 32.5.
To find the angle between vectors u = (8, -2) and v = (9, 3), we can use the dot product formula:
u · v = |u| * |v| * cos(theta)
where u · v represents the dot product of u and v, |u| and |v| represent the magnitudes of u and v respectively, and theta represents the angle between the vectors.
First, let's calculate the magnitudes:
|u| = sqrt(8^2 + (-2)^2) = sqrt(64 + 4) = sqrt(68) ≈ 8.246
|v| = sqrt(9^2 + 3^2) = sqrt(81 + 9) = sqrt(90) ≈ 9.486
Next, calculate the dot product:
u · v = 8 * 9 + (-2) * 3 = 72 + (-6) = 66
Now, we can rearrange the formula to solve for the angle theta:
cos(theta) = (u · v) / (|u| * |v|)
theta = arccos[(u · v) / (|u| * |v|)]
Substituting the values we calculated:
theta = arccos(66 / (8.246 * 9.486))
theta ≈ 32.5 degrees
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Please include a picture too and don’t do random answer!!!!! Use the drawing tool(s) to form the correct answers on the provided answer space.
Beth is tracking how many miles she walks in a week. Currently, she has walked one mile and plans to walk at a brisk pace of five miles
per hour for the rest of the week. Her brother Jonathan is also tracking the miles he walks in a week. He has already walked three miles
and plans to walk at a slower pace of three and a half miles per hour for the rest of the week.
The system of equations below represents the miles, y, walked by Beth and Jonathan in x hours.
y = 5x+1
y = 3 1/2x+ 3
Part A: Use the ray tool to graph the system of equations on the coordinate plane.
Part B: Use the point tool to select an approximate amount of time Beth and Jonathan will each have to walk this week in order for
them to have walked the same distance,
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Answer:
The graph is in the picture below. The correct amount of hours that it will take Beth and Jonathon to have walked the same distance is 1 3/8 miles.
Part A : The graph of the system y = 5x + 1 and y = (7/2)x + 3 is attached.
Part B : An approximate amount of time Beth and Jonathan will each have to walk this week in order for them to have walked the same distance is the common intersection point between these two graphs.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given, A system of equations for miles(y) and time(x) in hours Beth and Jonathan walked which is y = 5x + 1 and y = (7/2)x + 3.
The graph of the equation is attached in the image.
an approximate amount of time Beth and Jonathan will each have to walk this week in order for them to have walked the same distance is the common intersecting point between these two lines also attached in the second image attached.
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Which is an example of a quadratic trinomial
Answers
Answer:
Option 1 4x^3+6x^2-10x
Step-by-step explanation:
when the highest value for x has a cube root, it is a trinomial. Tri for 3. When it is squared it is a binomial. Bi for 2.
Hope that helps :)
what is the quotient of the expression
\( \frac{21a {}^{3} b - 14ab {}^{2} + 7ab}{7ab} \)
Answers
What is the resulting costant when (2 - 4/3) is subtracted from (-3/5 plus 5/3)
Answers
The resulting constant is 2/5 when (2-4/3) is subtracted from (-3/5 plus 5/3).
What is subtraction?Mathematical subtraction includes calculating the difference between two numbers. It is the inverse of addition and is denoted by the symbol "-". When we subtract one number from another, we are essentially finding out how much smaller the second number is than the first number.
According to question:We can simplify the expressions inside the parentheses first:
2 - 4/3 = 6/3 - 4/3 = 2/3
-3/5 + 5/3 = -9/15 + 25/15 = 16/15
So the expression (-3/5 + 5/3) - (2 - 4/3) becomes:
(16/15) - (2/3)
To subtract these fractions, we need to find a common denominator, which is the least common multiple of 15 and 3, which is 15. Then we can rewrite both fractions with this denominator:
(16/15) - (2/3) = (16/15) - (10/15)
Now we can subtract the numerators and keep the denominator:
(16/15) - (10/15) = 6/15 = 2/5
Therefore, the resulting constant is 2/5.
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6 mm
5 mm
13 mm
SA=
Rectangular Prisim
Answers
Answer:
346mm^2
Step-by-step explanation:
the formula to find the surface area of a rectangular prism is S.A.=2(l*w+l*h+w*h)
l is length
w is width
h is height
so, 2(13*6+13*5+6*5)
=346mm^2
Answer:
346 mm²
Step-by-step explanation:
Surface area of rectangular prism:l = length = 6 mm
w = width = 5 mm
h = depth = 13 mm
\(\boxed{\text{\bf Surface area of rectangular prism =2*(lw+wh+hl)}}\)
\(\sf = 2 *( 6*5 +5*13 +13*6)\\\\= 2* (30 + 65 + 78)\\\\= 2 * 173\\\\= 346 \ mm^2\)
Dawson simplifies the equation 4y-3=4(y + 1) and says it has no solution. Is dawson correct?
Answers
Let's start by substituting the right-hand side of the equation into the left-hand side:
What does the math equation mean?
Two expressions are combined by the equal sign to form a mathematical statement known as an equation. For instance, a formula might be 3x - 5 = 16. After solving this equation, we learn that the value of the variable x is 7.
4y - 3 = 4(y + 1)
4y - 3 = 4y + 4
Now, we can isolate y by subtracting 4y from both sides:
0 = y + 4
-4 = y
So, there is a solution to the equation: y = -4. This means that Dawson is incorrect in saying that the equation has no solution.
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Solve the following equation for z.
Answers
Answer: 6
Step-by-step explanation:
6 - 4 = 2
Im pretty sure the is the right answer! :)
Answer:
2 because
Step-by-step explanation:
2-4=2 yeah that all I got