Let T: Rn → Rn be an invertible linear transformation, and let S and U be functions from Rn into Rn such that

S(T(x)) = x and U (T(x)) = x for all x in R^n
Show that
U(v)= S(v) for all v in R^n

Required:
Compute S(v) and U(v).

Answers

Answer 1

Answer:

Follows are the solution to this question:

Step-by-step explanation:

[tex]T: 1 \ R^n \to 1 \ R^n[/tex] is invertible lines transformation

[tex]S[T(x)]=x \ and \ V[T(x)]=x \\\\t'x \ \varepsilon\ 1 R^n\\\\[/tex]

T is invertiable linear transformation means that is  

[tex]T(x) =A x \\\\ where \\\\ A= n \times n \ \ matrix[/tex]

and [tex]\ det(A) \neq 0 \ \ that \ is \ \ A^{-1} \ \ exists[/tex]

Let

[tex]V \varepsilon\ a\ R^{n} \ consider \ \ u= A^{-1} v \varepsilon 1 R^n\\\\T(u)= A(A^{-1} v)=(A \ A^{-1}) \\\\ v= I_{n \times n} \cdot v = v[/tex]

so,  

[tex]s[T(u)]=v[T(u)]\\\\s(v)=v(v) \ \ \forall \ \ v \ \ \varepsilon \ \ 1 R^n[/tex]


Related Questions

Suppose that the local sales tax rate is 7% and you purchase a car for $14,100

a. How much tax is paid ?
B. What is the car's total cost ?

Answers

I don't understand you're language

Clare bought a photo for 19 cents and paid with a $1 bill. How much change should she receive? ASAP

Answers

81 cents. :))))))))((()

Dario puts 44 marbles in a box in which 14 are red, 12 are blue, and 18 are yellow. If Dario picks one marble at random, what is the probability that he selects a red marble or a yellow marble?

Answers

Answer:

not simplified: 18/44    

Simplified: 9/22

Step-by-step explanation:

A security keypad uses five digits (0 to 9) in a specific order. How many different keypad patterns are possible if the first 4 digits must be even and the last digit cannot be zero, one or two?
Number of possible codes =

Answers

Answer:

g

Step-by-step explanation:

Multiply.
(3x + 1)(x + 7)

Answers

Answer:

the answer is 3x^2 + 22x + 7

Step-by-step explanation:

Expand the polynomial using the FOIL method.

hoped this helped!

brainly, please?

Answer:

3x^2+22x+7

Step-by-step explanation:

Help Asapppppppppppp

Answers

Answer:

(-15,0) and (0,-3)

Step-by-step explanation:

(-15,0) = x- intercept

(0,-3) = y-intercept

Kevin draws out one M&M without looking.

· What is P(green)?


· What is P(red)?


· What is P(~Yellow)?


· What is P(~Orange)?

Answers

Answer:

1/6

Step-by-step explanation:

M&M comes in 6 colors.

So, P(green), = 1/6

P(red) = 1/6

· P(Yellow) = 1/6

· P(Orange) = 1/6

nine times a number decreased by four

Answers

Answer: 9x - 4

Step-by-step explanation:

We know that a number must be decreased by four. Let's break it up a little.

Nine times some number. We don't know what nine will be multiplied by, so we will just write a placeholder number: x. This number will be multiplied by nine. So it will turn into 9x.

We must decrease (subtract) from this by four. Subtracting 9x by four can be written as 9x - 4.

The answer for this question is 9x-4

Find both the area and the perimeter of the semi circle

Answers

Answer/Step-by-step explanation:

Area of a semicircle = ½πr²

Perimeter of a semicircle = πr + d

7. d = 14 m

r = ½ of d = 7 m

Area = ½*π*7² = ½*π*49

✅Area = 76.97 m² (nearest hundredth)

Perimeter = π*7 + 14

✅Perimeter = 35.99 m (nearest hundredth)

8. d = 35 in.

r = ½ of d = 17.5 in.

Area = ½*π*17.5² = ½*π*306.25

✅Area = 481.06 in.² (nearest hundredth)

Perimeter = π*17.5 + 35

✅Perimeter = 89.98 in (nearest hundredth)

Suppose the half-life of a certain radioactive substance is 20 days and there are 50g present initially.
a)
Write an equation that models this situation.
b)
How much radioactive substance is remaining after 12 days?
c)
Find the time when there will be 1g of the substance remaining.

Answers

Answer:

a)   10(5g + 2r)   weight loss over time

b)   20/12 = 1.66667 = 50 / 1.67 = 29.999 gm = 5(6g -1/50)  or  5(5 + g) = 30g

c) 30g = 12 days = 3/5   therefore 5/5 -3/5 = 2/5  = 2/5 x 50 (g) = 20g in 8 days lost

8/20 = 0.4  loss each day 50g - 0.8g = 20-2 = 18 days.

Step-by-step explanation:

Helppppppp it’s due tomorrow

Answers

Answer:

A to f equals 2.5

A to e equals 1.5

a to d equals .5

a to c equals 2

a to I equals 3.5

a to g equals 3

a to h equals 4.5

a to j equals 4

a to k equals 5.5

use the big numbers as landmarks! that's the number before the decimal ( . ) to find the number after the decimal, count the little lines!

reatest to Smallest which is correct?



1. 50 16 5 -64


2. 16 5 50 -64


3. 5 16 -64 50


4. -64 50 16 5

Answers

Answer:

1. 50 16 5 - 64

Step-by-step explanation:

have a nice day

50, 16, 5, -64
Minus numbers are always the smallest for example;
-10 is smaller than -70 because it is closer to positive numbers eg: 1,2,3 eg

Which of the following does the graph below represent?
A. Ratios that are not equivalent
B. Equivalent ratios
C. Cannot tell from the graph

Answers

Answer:

Step-by-step explanation:

You cannot tell from the wiggly line! If that is supposed to be a straight line, you have equivalent ratios from point to point.

A full body treatment costs £125.00 Today there is a 10% discount, how much do you pay ?


Answers

Step-by-step explanation:

[tex] \frac{10}{100} \times 125 = 12.5 \\ 125 - 12.5 = 112.5[/tex]

112.5 £

112$ is how much you pay

Sumita buys a set of earphones for £12.17. She pays with £15. How much change does she get? Give your answer in £.

Answers

She will get $8.01. Hope this helped.

Simplify.
34x−7+2(x−2)

Answers

Answer:36x-11

Step-by-step explanation:

Answer: 36x-11

34x-7+2(x-2)

34x-7+2x-4

36x-11

Step-by-step explanation:

A company sells 100 - 0.5x shirts
when it charges %x per shirt. How
many dollars per shirt should the
company charge in order to make
$5,000 on shirt sales?​

Answers

Answer:

$100

Step-by-step explanation:

We are given that

Company sells shirts=100-0.5x

Charge per shirt=x

We have to find the  charge per shirt in order to make $5000 on shirt sales.

According to question

[tex]x(100-0.5x)=5000[/tex]

[tex]100x-0.5x^2=5000[/tex]

[tex]0.5x^2-100x+5000=0[/tex]

[tex]5x^2-1000x+50000=0[/tex]

[tex]x^2-200x+10000=0[/tex]

[tex]x^2-2\times x\times 100+(100)^2=0[/tex]

[tex](x-100)^2=0[/tex]

[tex]x=100,100[/tex]

Hence, charge per shirt=$100

A 1 km long train travelling at a speed of 60km/h enter a tunnel 1km long. What time will the train take to come out of the tunnel fully.​

Answers

Answer:

2 minutes

Step-by-step explanation:

The front of the train enters the tunnel and travels 1 km before the rear of the train enters the tunnel.  Thus, the total distance traveled by the front of the train is 2 km, and this is covered in a certain number of hours:

Since distance = rate times time, time = distance / rate.  In this particular case we have:

                                              2 km

time = distance / rate = ------------------- = (1/30) hr

                                           60 km/hr

(1/30) hr converts to 2 minutes, since 1 hr = 60 minutes

d = (4 x 180) - (3 x 90)

Answers

Answer:

d = (4 x 180) - (3 x 90) = 450

Step-by-step explanation:

d = (4×180) - (3×90)

d = (720) - (270)

d = 720 - 270

d = 450

HOPE THIS HELPS YOU

Follw me = 10 thanks

Mark as brainliest = 10 thanks

1 thanks to me = 2 thanks

5 x 1 3/45 * 1 3/4
What is the answer?​

Answers

Hopes this helps:

Answer: 9 1/3

Find the square root of the following decimal numbers.​

Answers

Answer:

[tex] \huge \boxed{ \tt i)1.6} \\ \huge \boxed{ \tt ii)4.3} \\ \huge \boxed{ \tt iii)8.3} \\ \huge \boxed{ \: \: \: \: \tt iv)9.2 \: \: \: }[/tex]

Step-by-step explanation:

to understand thisyou need to know about:square rootfinding square root by division methodconverting decimal to a fractionPEMDAStips and formulas:

tips for finding square root by division method

Group the digits in pairs, starting with the digit in the units placeThink of the largest number whose square is equal to or just less than the first period. Take this number as the divisor and also as the quotient.Subtract the product of the divisor and the quotient from the first period and bring down the next period to the right of the remainder. the new divisor is obtained by taking two times the quotient and annexing with it a suitable digit which is also taken as the next digit of the quotient, chosen in such a way that the product of the new divisor and this digit is equal to or just less than the new dividend. Repeat steps till all the periods have been taken up

tips for converting decimal to a fraction

Write down the decimal divided by 1Multiply both top and bottom by 10 for every number after the decimal pointreduce the fractionlet's solve:

solve the square roots using division method:

the picture is attached

solve the square roots by converting decimals into fraction:

[tex] \tt i) \sqrt{2.56} \\ \tt \sqrt{ \frac{256}{100} } \\ \tt \sqrt{ \frac{1 {6}^{2} }{ {10}^{2} } } \\ \tt\frac{16}{10} \\ \tt \: 1.6[/tex]

[tex] \tt ii) \sqrt{18.49} \\ \tt \sqrt{ \frac{1849}{100} } \\ \tt\sqrt{ \frac{ {43}^{2} }{ {10}^{2} } } \\ \tt \frac{43}{10} \\ \tt 4.3[/tex]

[tex] \tt iii) \sqrt{ 68.89} \\ \tt \sqrt{ \frac{6889}{100} } \\ \tt \sqrt{ \frac{ {83}^{2} }{ {10}^{2} } } \\ \tt \frac{83}{10} \\ \tt 8.3[/tex]

[tex] \tt iv) \sqrt{84.64} \\ \tt\sqrt{ \frac{8464}{100} } \\ \tt\sqrt{ \frac{ {92}^{2} }{ {10}^{2} } } \\ \tt \frac{92}{10} \\ \tt9.2[/tex]

Answer:

1.6

4.3

8.3

9.2

Step-by-step explanation:

Hope it is helpful....

A bag contains 1 dollar, 50 cents and 25 cents coins in the ratio 3:5:7. The total amount is $ 1856.
Find the number of each denomination.​

Answers

Answer:

There are 768 1 dollar coins, 1280 50 cent coins and 1792 25 cent coins

Step-by-step explanation:

The total amount of coins is given by x.

Ratio 3:5:7

[tex]\frac{3}{3+5+7} = \frac{3}{15}[/tex] are worth $1.

[tex]\frac{5}{3+5+7} = \frac{5}{15}[/tex] are worth 50 cents = $0.5.

[tex]\frac{7}{3+5+7} = \frac{7}{15}[/tex] are worth 25 cents = $0.25.

The total amount of money is $1856.

This means that:

[tex]\frac{3x}{15} + 0.5\frac{5x}{15} + 0.25\frac{7x}{15} = 1856{/tex]

Multiplying everything by 15

[tex]3x + 2.5x + 1.75x = 27840[/tex]

[tex]7.25x = 27840[/tex]

[tex]x = \frac{27840}{7.25}[/tex]

[tex]x = 3840[/tex]

Amount of coins of 1 dollar:

[tex]\frac{3*3840}{15} = \frac{3840}{5} = 768[/tex]

Amount of 50 cent coins:

[tex]\frac{5*3840}{15} = \frac{3840}{3} = 1280[/tex]

Amount of 25 cent coins:

[tex]\frac{7*3840}{15} = 1792[/tex]

There are 768 1 dollar coins, 1280 50 cent coins and 1792 25 cent coins

Each year the US Environmental Protection Agency (EPA) releases fuel economy data on cars manufactured in that year. Below arc summary statistics on fuel efficiency (in miles/gallon) from random samples of cars with manual and automatic transmissions manufactured in 2012. Do these data provide strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage?

Answers

Answer:

Follows are the solution to this question:

Step-by-step explanation:

Please find the complete question in the attachment file.

[tex]n_1 = 26 \\\\ x_1 = 16.12 \\\\s_1 = 3.58\\\\n_2 = 26\\\\ x_2 = 19.85 \\\\ s_2 = 4.51[/tex]

[tex]H_0: u_1 = u_2\\\\H_1: u_1 \neq u_2[/tex]

Using formula:

[tex]\to S^{2}_{p}=\frac{S^{2}_{1}(n_1 -1)+ S^{2}_{2}(n_2-1)}{n_1+n_2-2}[/tex]

[tex]\to Sp^2 = \frac{((26-1) \times (3.58^2) + (26-1) \times (4.51^2))}{(26+26-2)}[/tex]

          [tex]= \frac{((25) \times 12.8164 + (25) \times 20.3401 )}{(26+24)}\\\\ = \frac{(320.41 + 508.5025)}{(50)}\\\\ = \frac{(828.9125)}{(50)}\\\\=16.57825[/tex]

[tex]\to Sp = 4.0716[/tex]

Calculating the value of standard error:

[tex]\to SE = Sp \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}[/tex]

          [tex]=4.0716 \times \sqrt{\frac{1}{26}+\frac{1}{26}}\\\\=4.0716 \times \sqrt{\frac{1+1}{26}}\\\\=4.0716 \times \sqrt{\frac{2}{26}}\\\\=4.0716 \times \sqrt{\frac{1}{13}}\\\\=4.0716 \times 0.277 \\\\=1.1278332\\\\= 1.1293[/tex]

Calculating the value of test statistic:

Formula:

[tex]\to t = \frac{(x_1-x_2)}{SE}[/tex]

      [tex]= \frac{(16.12 -19.85)}{1.1293}\\\\= \frac{(-3.73)}{1.1293}\\\\=-3.303[/tex]

Calculating the value of Degree of freedom:

[tex]= n_1+n_2 -2 \\\\= 26+26 -2 \\\\= 52 -2 \\\\= 50[/tex]

Because the P-value is a 2-tailed test = 0.0018

Thus they reject H0, because of P-value < 0.05,

Yeah, certain data show clearly that the means are different.



please help. It’s really easy just the question is worded weirdly and I don’t get it.

Answers

Answer:

d

Step-by-step explanation:

Nigel has 138 fluid ounces of lemonade. How many 6-fluid-ounce serving of lemonade can he make​

Answers

Answer:

23, because 138 divided by 6 is 23

He can make 23 servings.

plz help me brainlest for the 1st answer

Answers

The answer is a medium Pizza of 12 inches radius.

The formula for finding the area of a square is pir^2(sorry but my phone won’t let me write pi in its symbol form). If we substitute 3 for pi, then that would the 3r^2. Then we would substitute the potential answer choices until we reach one that is closest to 400 in^2. For the small pizza, that would be 9*9*3, which is also 243 inches square. For the medium pizza, that would be 12*12*3, which is also 432 inches square. Finally, for the large pizza it is 15*15*3, which is 675. Therefore, the medium pizza has an area closest to inches square.

Aliyah's school is selling tickets to a play. On the first day of ticket sales the school sold 9 adult tickets and 14 student tickets for a total of $220. The school took in $188 on the second day by selling 11 adult tickets and 7 student tickets. What is the price each of one adult ticket and one student ticket? Write answer as an ordered pair.

Answers

Answer:

Step-by-step explanation:

a and s are the numbers of adult and student tickets, respectively.

9a + 14s = 220

11a + 7s = 188 Multiply by -2 and add to first equation.

-22a - 14s = -376

9a + 14s = 220

-----------------------

-13a = -156

a = 12

9(12) + 14s = 220

14s = 112

s = 8

Adult tickets cost $12. Student tickets cost $8.

can someone please help me with this math problem thank you.

Answers

The perimeter is 10.25 by adding all sides of the triangle. Using the formula for a triangle, (height times base)/2, the area is 5.
A). 10.25
B). 5 (I think)

A square has sides of 10x. Write and simply an expression for the perimeter square

Answers

10X x 4= 40x
.........................
=40x

Answer:

4(10x) = 40x

Step-by-step explanation:

Assuming you meant that each side has 10x, and not the sum of each side is 10x. Since each side has 10x, and every square has equal sides of 4, we can utilize parenthesis.

4 = number of sides

10x = given length of each side

4(10x) = 40x

Same as saying 4 × 10x = 40x.

The function f(x) is defined below. What is the end behavior of f(x)?

Answers

Answer:

first choice

Step-by-step explanation:

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