Question 3: (5+2+5 Marks) Let S= i) Show that S is linearly independent. ii) Deduce that S is a basis for M₂2- iii) Express A as a linear combination of the vectors in S and find (A)s, where A re A = [ {[H[H²H]} 24 <-151
We are given a set of vectors S in M₂₂ and we need to show that S is linearly independent. We then deduce that S is a basis for M₂₂. Additionally, we are asked to express vector A as a linear combination of the vectors in S and find the coordinates of A with respect to the basis S.
To show that S is linearly independent, we need to demonstrate that the only solution to the equation c₁v₁ + c₂v₂ + c₃v₃ = 0, where c₁, c₂, and c₃ are scalars, is c₁ = c₂ = c₃ = 0. Here, v₁, v₂, and v₃ are the vectors in S.
Let's consider the vectors in S:
v₁ = {[H, 3H, H]}
v₂ = {[H², H], 24}
v₃ = {[-15, 1], 5}
To show linear independence, we set up the equation c₁v₁ + c₂v₂ + c₃v₃ = 0 and solve for c₁, c₂, and c₃.
c₁{[H, 3H, H]} + c₂{[H², H], 24} + c₃{[-15, 1], 5} = 0
By comparing the corresponding entries on both sides of the equation, we obtain the following system of equations:
c₁H + c₂H² - 15c₃ = 0
3c₁H + c₂H + c₃ = 0
c₁H + 24c₂ + 5c₃ = 0
We can solve this system of equations to find c₁, c₂, and c₃. If the only solution is c₁ = c₂ = c₃ = 0, then S is linearly independent.
To deduce that S is a basis for M₂₂, we need to show that S is linearly independent and spans the entire space M₂₂. Since we have shown linear independence, we now need to demonstrate that S spans M₂₂. To do this, we need to show that any matrix in M₂₂ can be expressed as a linear combination of the vectors in S.
Finally, to express vector A = {[-15, 1], 5} as a linear combination of the vectors in S, we solve the equation c₁v₁ + c₂v₂ + c₃v₃ = A for the coefficients c₁, c₂, and c₃. Once we find the coefficients, we can write (A)s to represent the coordinates of A with respect to the basis S.
In conclusion, to summarize the answer, we have shown that S is linearly independent, which implies that S is a basis for M₂₂. We can express vector A as a linear combination of the vectors in S and find its coordinates with respect to the basis S. However, the specific calculations to find the coefficients and coordinates are not provided in the question.
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factorize: 3x^3-13x^2+16
My teacher is super picky about this type of stuff and I’m not sure how I would do it... Please show steps when solving for slices of pizza!
SHOW YOU WORK TO BE MARKED BRAINLIEST!!!
Answer: x=65
Step-by-step explanation:
Set (2x + 2) equal to (3x-63) because they are the same angle.
(2x+2)=(3x-63)
Subtract 2x from 3x which gives u 1x or just x
Now u have 2=x-63
Add 63 to both sides so now u have x =65
Lemme know if u need help
The figure below was made with a scale of 1 unit =9 m. You can place your figure anywhere on the grid on the right.
Answer & Step-by-step explanation:
I can't draw the image, but I can explain it to you.
Since 1 unit was 3 units and now it's 9, you would have to divide each side by 3. So, the width would be 1 unit and the length would be 2 units.
I hope this helped!!!
The scale of 1 unit = 9 m
The rectangle 1 unit = 3 m is similar to 1 unit = 9 m
Since the unit of the scale is reduced the image size will be smaller than the given diagram.
What is supposed by similarity in math?In Euclidean geometry, objects are comparable if they have an identical shape, or if one has the same form because they reflect a photograph of the other. more precisely, one can be obtained from the opposite by using uniformly scaling (enlarging or lowering), probably with extra translation, rotation and reflection.
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PLEASE HURRY TONS OF POINTS!!
Allie bought a used car in 2011 with 19,800 miles on it. In 2016, she had 500 more than four times
the number of miles that were on it when she purchased it. Find the rate of change in miles from 2011 to 2016
A. 9,980 miles per year C. 10,760 miles per year
B. 10,175 miles per year D. 11,980 miles per year
Answer:
the answer is b I did the math
–3m − 6 = –4m
find m please
Answer:
m=6
Step-by-step explanation:
-3m+4m=6
m=6
Answer:
m= 6
Step-by-step explanation:
-3m - 6 = -4m
-6 = -m
the "m" cannot be negative soooo
6 = m
Alba is Saving for a big overseas trip she hopes to take her senior year in college , which is four years away . She plans to deposit 10,000 at the end of each quarter in an account earning 8% annual interest , compounded quarterly . How much money will alba have for trip after 20 years ?
Answer:
FV= $1,937,719.58
Step-by-step explanation:
Giving the following information:
Quarter deposit= $10,000
Number of periods= 20*4= 80
Interest rate? 0.08/4= 0.02
To calculate the future value, we need to use the following formula:
FV= {A*[(1+i)^n-1]}/i
A= quarter deposit
FV= {10,000*[(1.02^80) - 1]} / 0.02
FV= $1,937,719.58
Simplify |-3 - 6·2|
Answer:
9.2
Step-by-step explanation:
= | (-3) - 6.2 |
= | -9.2 |
= 9.2
Answer:
-15 because first mutipli 6 and 2 then - 3 subtracted by 12
Solve the problems. Write the complete proof in your paper homework and for online (only) respond to questions or statements (if any) that are parts of your proof or related to it. Given: AB = AC m∠1=m∠2 AC = 15, DC = 5 Find: BD, AB
Answer:
AB=15 BD=18
Step-by-step explanation:
AB is 15 because AB=AC and AC is 15
BD:
Using the Pythagorean Theorem
10²+15²=√325
√325=18
10 is from AB-CD
15 is the height which is AC
Answer:
BD = 5, and AB = 15 :)
write a formula for the given measure. tell what each variable represents. identify which variable depends on which in the formal. the perimeter of a rectangle with the length of 5 inches
Sure, here is the formula for the perimeter of a rectangle with a length of 5 inches:
Perimeter = 2(5 + w)
where:
Perimeter is the total length of all the sides of the rectangle, in inches
5 is the length of one side of the rectangle, in inches
w is the width of the rectangle, in inches
The variable w depends on the variable 5, because the width of the rectangle cannot be greater than the length of the rectangle.
Here is an example of how to use the formula:
If the length of the rectangle is 5 inches and the width is 3 inches, then the perimeter is:
Perimeter = 2(5 + 3)
= 2(8)
= 16 inches
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a box has 10 disks numbered 1 through 10. a disk is drawn at random 50 times with replacement. the disk numbered 7 was drawn 6 times. what is the relative frequency of getting the disk numbered 7 on the next draw?
The relative frequency of getting the disk numbered 7 on the next draw is 0.12 or 12%.
To find the relative frequency of getting the disk numbered 7 on the next draw, we need to analyze the data provided.
In this scenario, a disk is drawn at random from a box containing 10 disks numbered 1 through 10. The draws are made with replacement, meaning that after each draw, the disk is returned to the box, and the next draw is independent of the previous ones.
We are given that the disk numbered 7 was drawn 6 times out of the 50 draws. To find the relative frequency of getting the disk numbered 7 on the next draw, we need to determine the proportion of times it appeared relative to the total number of draws.
The relative frequency can be calculated by dividing the number of times the desired outcome occurs (in this case, drawing disk 7) by the total number of trials (draws).
In this case, the number of times disk 7 was drawn is 6, and the total number of draws is 50. Therefore, the relative frequency is:
Relative frequency = (Number of times disk 7 was drawn) / (Total number of draws)
= 6 / 50
= 0.12
Hence, the relative frequency of getting the disk numbered 7 on the next draw is 0.12 or 12%.
This means that if we were to continue drawing disks with replacement, the probability of drawing disk 7 on the next draw would be approximately 12%. However, it's important to note that since the draws are made with replacement, the probability of drawing any specific disk remains the same for each draw, regardless of the previous outcomes.
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PLEASE HELP ASAP
Determine the x-intercept, y-intercept, and slope of the line described by −3x+7y=−21
Please state what the x-intercept, y-intercept, and slope is!!!
Answer:
Slope = 3/7
y - intercept: y = -3
x - intercept x = 7
Step-by-step explanation:
You have to cimplify the equation in terms of y
-3x +7y= -21
7y= 3x-21
y = 3/7x - 3
SLOPE: It is whatever x is mutlipliedby
slope would be 3/7
Y intercept: you need to plug in x=0
y = 3/7(0) - 3
Zero multipled by anything is zero so you are left with
y = -3
X intercept: plug in y = 0
0 = 3/7x - 3
Move the -3 to the other side
3 = 3/7x
Multiply by the reciprocal 7/3
x = 7/3 * 3
x = 21/3
x = 7
how????
2 1/3 divided by 1/4
Answer:
9.3
Step-by-step explanation:
what's that 2 i just don't understand that buddy??
2) Suppose the probability distribution for the one-period return of some asset is as follows: Return Probability 0.27 0.25* 0.18 0.25* 0.10 0.30 p.04 0.20+ a. What is this asset's expected one-period
The expected one-period return for the asset is given by the expression 0.0675 + 0.045 + 0.03 + 0.04p + 0.04, where 'p' represents an unknown probability.
The given probability distribution represents the one-period return for an asset, with corresponding probabilities assigned to each return value. To find the expected one-period return, we need to calculate the weighted average of the returns, where the weights are the probabilities.
Let's calculate the expected one-period return step by step:
1. Multiply each return value by its corresponding probability:
0.27 * 0.25 = 0.0675
0.18 * 0.25 = 0.045
0.10 * 0.30 = 0.03
p * 0.04 = 0.04p
0.20 * 0.20 = 0.04
2. Sum up the products calculated in step 1:
0.0675 + 0.045 + 0.03 + 0.04p + 0.04
3. Set the sum equal to the expected one-period return, denoted as E(R):
E(R) = 0.0675 + 0.045 + 0.03 + 0.04p + 0.04
Therefore, the expected one-period return of the asset is 0.0675 + 0.045 + 0.03 + 0.04p + 0.04.
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i need help for this? 4-{-8}/8+5=
Answer:
If you have put the bracket/parenthesis correct, then
4 - {-8}/8 + 5
=> 4 - (-1) + 5
=> 4 + 1 + 5
=> 5 + 5
=> 10
If my answer helped, kindly mark me as the brainliest!!
Thank You!!
Which postulate or theorem can be used to determine the length of RT
Answer:
AAS Congruence Theorem
Step-by-step explanation:
The two triangles share the same vertex T. Therefore, both ∆s has the same measure of <T.
From the information made available in the diagram above, it shows that the non-included side of 170, and two given angles, <T and <S in ∆RST are congruent to the non-included side of 170, and two given angles, <T and <U in ∆VUT. Therefore, ∆RST and ∆VUT are both congruent to each other based on the AAS Congruence Theorem.
This invariably implies that the length of RT is congruent to the length of VT.
What was the first ever Marvel comic book and when was made?
Answer:
The fantastic four in 1961
can you help me on quadratic equation?
the legth of a swimming pool is 8m longer than its width and the area is 105 m2
Step-by-step explanation:
Let the width be x ,
then length=(8+x),
A/Q,
l×b = area
=>x×(8+x)=105
=>8x+x²=105
=>8x+x=√105
=>9x=√105
=>9x=10.246950765959598
x=1.138550085106622
pls help 100 points, fast as possible
Answer:
-2 divided by 2
Step-by-step explanation:
Answer:
Using Slope intercept form :
y = mx + c
Here, m = (- 2 /-2) = 1 and c = - 2
Therefore,
y = x - 2
Leo just bought a guitar signed by Gene Simmons. The shape of the body is a triangle with a base of
14 inches and a height of 18 inches. The neck of the guitar is 3 inches X 21 inches.
What is the total area of Leo's new guitar?
Answer:
[tex]189in^2[/tex]
Step-by-step explanation:
[tex]\frac{14*18}{2}=\frac{252}{2}=126[/tex]
[tex]3*21=63[/tex]
[tex]126+63=189[/tex]
Can someone help me with this question plz?
Answer:
cant see pic
Step-by-step explanation:
You invest $3,287 in a savings account with a fixed annual interest rate of 9% compounded monthly. What is the account balance after 4 years?
Answer: I’m pretty sure that it’s 14199.84
Step-by-step explanation:
.09 times 48 is 4.32
4.32 times 3287 is 14199.84
You get the 48 from 12 months per year for 4 years
A scientist counts the number of inclusions in a sample of 30 tourmaline rocks, each of weight 50g. a If the sample mean number of inclusions per gem is 31.0635 and the sample standard deviation of the number of inclusions is 2.0996, calculate the standard error of the mean number of inclusions. (Please provide answers rounded to four decimal places) Submit part Score: 0/1 Unanswered b) Use you answer from the previous question to estimate a 95% confidence interval for the mean number of inclusions per tourmaline gem (Please provide your answer to four decimal places).
a) To calculate the standard error of the mean number of inclusions, we divide the sample standard deviation by the square root of the sample size. In this case, the sample mean number of inclusions is 31.0635, and the sample standard deviation is 2.0996. The sample size is 30. Therefore, the standard error of the mean number of inclusions can be calculated as follows:
Standard Error = Sample Standard Deviation / √Sample Size
Standard Error = 2.0996 / √30 Standard Error ≈ 0.3836 (rounded to four decimal places) b) To estimate a 95% confidence interval for the mean number of inclusions per tourmaline gem, we can use the formula: Confidence Interval = Sample Mean ± (Critical Value × Standard Error) The critical value corresponds to a 95% confidence level, which is 1.96 for a large sample size. Using the standard error calculated in part (a) as 0.3836 and the sample mean of 31.0635, the confidence interval can be calculated as: Confidence Interval = 31.0635 ± (1.96 × 0.3836)
Confidence Interval ≈ 31.0635 ± 0.7521 Confidence Interval ≈ (30.3114, 31.8156) (rounded to four decimal places) Therefore, we can estimate with 95% confidence that the mean number of inclusions per tourmaline gem lies between approximately 30.3114 and 31.8156.
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A runner covers the last stretch of a race in 4 seconds, during that time he speeds up from 5 m/s to 9 m/s what is the runners acceleration from this part of the race?
Answer:
1m/s^2
Step-by-step explanation:
the formula for acceleration is change in velocity divided by time
the change in velocity is 4m/s (subtract 5 from 9)
the change in time is 4 seconds
so 4m/s ÷ 4s
this gives you 1m/s^2
can someone help me on this plz
The diameter of the Sun is about 1.4 x 10^6 km. The diameter of the planet
Mercury is about 5000 km.
What is the approximate ratio of the diameter of the Sun to the diameter of
Mercury?
A. 2.8 x 10^2
B. 3.6 x 10^-3
C. 3.6 x 10^2
D. 2.8 x 10^3
Answer:c
Step-by-step explanation:
The approximate ratio of the diameter of the Sun to the diameter of
Mercury 3.6 x 10^-3.
We have given that,
The diameter of the Sun is about 1.4 x 10^6 km.
The diameter of the planet Mercury is about 5000 km.
We have to determine the approximate ratio of the diameter of the Sun to the diameter of Mercury.
What is the diameter?
A circle's diameter is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the most extended chord of the circle. Both definitions are also valid for the diameter of a sphere.
The approximate ratio of the diameter of the Sun to the diameter of
Mercury 3.6 x 10^-3.
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without solving explain why the equations do not have solutions
We have 2 terms:
[tex]\sqrt{x+2}[/tex] and [tex]\sqrt{4x+1}[/tex]
For the sum of these to equal a negative number, in this case -3, one of these terms would have to be negative.
So what's the problem?The function [tex]\sqrt{x}[/tex] (square root of x) only returns positive values!
(See the attached image for a graph of [tex]\sqrt{x}[/tex])
Since neither of the terms can be negative, it can't be equal to -3. In other words, no matter what we put as [tex]x[/tex], we can't solve the solution, so we say that the equation does not have any solutions.
what do you get when u count out 40 dollars with quarters?
help me please
Answer:
160 Quarters
Step-by-step explanation:
There are 4 quarters in a dollar, and we know that there are 40 dollars. Multiply 40 by 4 to get 160
Hope this helps :-)
What is the solution set for the equation 2|-3n| + 10 = 50
I
Answer:
[tex]n=-\frac{20}{3}\quad \mathrm{or}\quad \:n=\frac{20}{3}[/tex]
Step-by-step explanation:
[tex]2\left|-3n\right|+10=50\\\\\mathrm{Subtract\:}10\mathrm{\:from\:both\:sides}\\\\2\left|-3n\right|+10-10=50-10\\\\Simplify\\\\2\left|-3n\right|=40\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\\frac{2\left|-3n\right|}{2}=\frac{40}{2}\\\\Simplify\\\\\left|-3n\right|=20\\\\\mathrm{Apply\:absolute\:rule}:\\\quad \mathrm{If}\:|u|\:=\:a,\:a>0\:\mathrm{then}\:u\:=\:a\:\quad \mathrm{or}\quad \:u\:=\:-a\\[/tex]
[tex]-3n=-20\quad \mathrm{or}\quad \:-3n=20\\\\-3n=-20\quad :\quad n=\frac{20}{3}\\\\-3n=20\quad :\quad n=-\frac{20}{3}\\\\n=-\frac{20}{3}\quad \mathrm{or}\quad \:n=\frac{20}{3}[/tex]
