Show that the transformation T defined by
T(x1, x2) = (2x1 - 3x2, X1+4, 5x2) is not linear.

Answers

Answer 1

Let u = (1, 0) and v = (0, 1). Then

T (u) = (2*1 - 3*0, 1 + 4, 5*0) = (2, 5, 0)

T (v) = (2*0 - 3*1, 0 + 4, 5*1) = (-3, 4, 5)

=>   T (u) + T (v) = (-1, 9, 5)

but

T (u + v) = T (1, 1) = (2*1 - 3*1, 1 + 4, 5*1) = (-1, 5, 5)

=>   T (u + v) ≠ T (u) + T (v)

which means T does not preserve addition, so it is not linear.


Related Questions

Someone please help!

Answers

264 in. I believe. If you multiply them all
The answer is 290. The previous answer is incorrect because they calculated volume. The question asks for SURFACE AREA.

Plz help me well mark brainliest if correct

Answers

Answer:

I think it is b) 70

Step-by-step explanation:

Arrange the numbers in ascending order then find the middle number.

Answer:

70

Step-by-step explanation:

Write down all the data points: 20, 40, 50, 70, 80, 90, 110 and identify which is in the very middle.

Solve for X. Round to the nearest tenth of a degree, if necessary.
7.9
4.1
R
S.

Answers

Answer:

30

Step-by-step explanation:

this is a right triangle which is 30 60 90 and the smaller angle is always 30

Answer: 59.7

Step-by-step explanation:

if m<1=25 what is the measure of an angle that is complementary to <1

Answers

Answer:

65°

Step-by-step explanation:

The sum of the measures of complementary anfglwes is 90°.

Let a = the measure of the complement.

m<1 + a = 90

25 + a = 90

a = 65

An investment of $8500 increases in value by 4.5% every year. How long until the investment
reaches about $17,323. Round to the nearest whole year

Answers

Answer:

17 years

Step-by-step explanation:

We can use a known formula (n being the number of years)

n = log(17323/8500) / log (1+ 0.045) = 16.17

On Friday night, the owner of Chez Pierre in downtown Chicago noted the amount spent for dinner for 28 four-person tables.
95 103 109 170 114 113 107 124 105 80 104 84 176 115 69 95 134 108 61 160 128 68 95 61 150 52 87 136
(a) Find the mean, median, and mode.
(b) Do these measures of center agree? Explain.
(c) Make a histogram or dot plot.
(d) Are the data symmetric or skewed? If skewed, which direction?

Answers

Answer:

median: 104.5

mean: 102.4

mode: 95

Step-by-step explanation:

A system of equations is shown below: y = 8x − 2 y = 9x − 7 What is the solution to the system of equations? (1 point) (−5, 38) (−5, −38) (5, 38) (5, −38)

Answers

Answer:

(5,38)

Step-by-step explanation:

Use graphing calculator and the answer should be the point where the line crosses each other.

Answer:

5,38

Step-by-step explanation:

its correct!

somebody help me and show your work pls

Answers

Answer:

40x(14)

Step-by-step explanation:

5x(2)y(0)(2x(4)(3)

5x(2)x1) x8x(12)

5x(2)x8x(12)

40x(14)

10.3.23
Question Help
o
In a recreation center with 1,500 members, 200 are high school students. Of the members, 300 regularly swim. The 45 students of the high school swim team are
all members and practice at the pool every week. What is the probability that a high school member selected at random is on the swim team?
The probability is
o
(Simplify your answer.)

Answers

Answer:

The probability that a high school member selected at random is on the swim team is [tex]\frac{9}{40} = 0.225[/tex]

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: High school student.

Event B: Is on the swin team.

Probability of selecting a high school student:

Of the 1500 students, 200 are on high school. So

[tex]P(A) = \frac{200}{1500}[/tex]

Probability of selecting a high school student who swims:

Of the 1500 students, 45 are high school students who swim. So

[tex]P(A \cap B) = \frac{45}{1500}[/tex]

What is the probability that a high school member selected at random is on the swim team?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{45}{1500}}{\frac{200}{1500}} = \frac{45}{200} = \frac{9}{40} = 0.225[/tex]

The probability that a high school member selected at random is on the swim team is [tex]\frac{9}{40} = 0.225[/tex]

i need help asap thank you

Answers

Answer:G

Step-by-step explanation:Since it is decreasing in size, the coordinates have to be negative so the only answer is G

Which statement is given in the diagram?

Answers

Answer:

D

Step-by-step explanation:

Plz help plz "??????????????

Answers

the answer is a. john

hope this helps!
john
have a good day x


A. Match the given solid figures to its corresponding formulas. Write the
letter of the correct answer in the blank.

please help​

Answers

This is a Right answer....

Question 6 of 10
Classify the following triangle. Check all that apply.
O A. Isosceles
B. Equilateral
O C. Obtuse
D D. Scalene
E. Right
OF Acute
SUB

Answers

Answer: a b f

Step-by-step explanation: I need brainliest for next rank I’d appreciate it

i believe it is A, B, and F good luck.

The graph of f(x) - 3* -6 is shown below. g() is a transformation of f(x).
How would you write the equation for the function g(x)?
15
10
5+
g(x)
is 2015 16
f(x) = 13*-6 -10
5
10
15 20 25
5
15+
O
A. g(x) - 3* +2
B. g(x) =
Ο Ο
2--13*-6
c. g(x)=13* +3
D. g(x)= - 4*+3
o

Answers

Answer:

[tex]g(x) = \frac{1}{4}3^x +3[/tex]

Step-by-step explanation:

Given

[tex]f(x) =\frac{1}{4}3^x -6[/tex]

[tex]g(x) \to[/tex] translate f(x) 9 units up

Required

Find g(x)

The translation rule is:

[tex]g(x) \to f(x) + 9[/tex]

So, we have:

[tex]g(x) = f(x) + 10[/tex]

[tex]g(x) = \frac{1}{4}3^x - 6 + 9[/tex]

[tex]g(x) = \frac{1}{4}3^x +3[/tex]

What are the zeros of the function f(x) = x2 – 10x + 21?
help bro

Answers

Answer:

3, 7

Step-by-step explanation:

"Zeros" means solutions to the equation f(x) = 0.  In other words, what are the values of  x  that make the function's value equal to zero?

This one can be solved by factoring.

[tex]x^2-10x+21=0\\(x-7)(x-3)=0\\x-7=0 \text{ or } x-3=0\\x=7 \text{ or } x=3[/tex]

PLEASE HELPPPPPPPPP MEEE!​

Answers

Let's calculate

4/15×285 + 3/20×320 = 124

124 students are participating in these exercises.

7 students is participating

Raden says that a trapezoid is a
quadrilateral because it has four sides.
Amanda says that a trapezoid is a
parallelogram because it has a pair of
parallel sides. Who is correct? Explain.

Answers

Answer:

Raden is correct

Step-by-step explanation:

A quadrilateral is any polygon that has four sides and four angles.

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides and angles of a parallelogram are equal. Also, the diagonals are equal to each other and bisect each other.

A trapezoid is a quadrilateral with atleast a pair of parallel sides. It has no perpendicular sides or right angles.

Raden is correct because a trapezoid is a quadrilateral since it has four sides. Amanda is not correct because for a trapezoid to be a parallelogram it must have two pairs of parallel sides and not just a single pair of parallel side.

If 4, m & 9 are in continued proportion. Find the value of m.​

Answers

Answer:

M =6

Step-by-step explanation:

T2/T1=T3/T2

M/4=9/m

M^2=36

M=+ or - 6

As m is continued ignore - 6

Then get m =6

How do you simplify √(29-12 √5)?

Answers

Answer:

2 sqaure root 5 -3

Step-by-step explanation:

See the Image below:)

(2[tex]\sqrt{5}[/tex] - 3)

What is simplification?

The process of replacing a mathematical expression with one that is equivalent, simpler, and typically shorter. Examples of simplification include simplifying algebraic expressions in computer algebra, simplifying Boolean expressions in logic optimization, and simplifying by conjunction elimination in logic inference to produce a formula that is simpler but typically non-equivalent.

Given equation  [tex]\sqrt{(29 - 12\sqrt{5}) }[/tex]

[tex]\sqrt{(29 - 12\sqrt{5}) }[/tex] = [tex]\sqrt{(9 + 20 - 2 x 3 x 2\sqrt{5}) }[/tex]

=  [tex]\sqrt{(3^{2} + (2\sqrt{5} )^{2} - 2 x 3 x 2\sqrt{5}) }[/tex]...…(1)

the equation is now in the form of (a - b)² =  a² + b² + 2ab

equation (1) can be written as where a =  2√5 and b = 3

[tex]\sqrt{(2\sqrt{5} - 3 )^{2} }[/tex] = 2√5 - 3

Hence the simplified equation is  2√5 - 3

Learn more about simplification;

https://brainly.com/question/23509407

#SPJ2

65 inches is how many feet? (Round to nearest hundredth) *

Answers

Answer:

5.42 feet

Step-by-step explanation:

12 inches=1 foot

65/12=5.41667

5.41667=5.42 feet

Answer:

5.42 feet

Step-by-step explanation: i hope its right and sorry if it's wrong

https://www.amphi.com/cms/lib/AZ01901095/Centricity/Domain/4604/6th%20ELA%20website%20040620.pdf
I HELP FOR THIS ANSWER THIS ANSWERS
THIS FOR GRADE PLEASE HELP

Answers

Answer:

I tried but it said 4 0 4 e r r o r i d k why

Step-by-step explanation:

a rectangle has a base of 10 and a height of 12 what is it area

Answers

Answer:

120

hope this helps

have a good day :)

Step-by-step explanation:

120 if not that 60

Step-by-step explanation:

hope this helped

leo le debe 15.00 pesos. Si su madre le da 60.00 pesos de paga y se gasta 20.00 con sus amigos
¿cuanto dinero le queda?
¿tendrá pendiente alguna deuda?

Answers

Answer:

Le quedan 25 pesos

No tendrá pendiente ninguna deuda

Step-by-step explanation:

60-15-20=25

Make a the subject of the formula.
please help asap!!!!!​

Answers

Answer:

Step-by-step explanation:

W=[tex]\sqrt{x-a/a}[/tex]

squaring both sides

W^2=([tex]\sqrt{x-a/a}[/tex] )^2

W^2=x-a/a

wa=x-a

a=x-a/w

[tex] \boxed{\boxed{\huge{ \mathrm{  \underline{ Answer} \:  \:  ✓ }}}}[/tex]

[tex]w = \sqrt \dfrac{{x - a} }{a} [/tex]

[tex]w {}^{2} = \dfrac{x - a}{a} [/tex]

[tex]w {}^{2} = \dfrac{x}{a} - \dfrac{a}{a} [/tex]

[tex]w {}^{2} = \dfrac{x}{a} - 1[/tex]

[tex] {w}^{2} + 1 = \dfrac{x}{a} [/tex]

[tex] \dfrac{1}{w {}^{2} + 1 } = \dfrac{a}{x} [/tex]

[tex]a = \dfrac{x}{ {w}^{2} + 1 } [/tex]

_____________________________

[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]

will give brainliest if u answer this right^ p-20=46

Answers

Answer:

you forgot to link the photo

Step-by-step explanation:

Answer:

66

Step-by-step explanation:

p-20=46

p= 46+20

p=66

Any help at all would be appreciated!

Answers

Answer:

√24

Step-by-step explanation:

Answer:

[tex] \sqrt{24} [/tex]

as

[tex] \sqrt{25} = 5[/tex]

so

[tex] \sqrt{24} \: is \: nearly \: equal \: to \: 5[/tex]

also it is smaller than 5 and the number shown on the number line is left to 5 so it must be smaller than 5

How many solutions are there to this equation?
3(3x−1)=6x−3

A. no solutions B. one solution C. two solutions D. infinite solutions

Answers

Answer:

B. One solution

Step-by-step explanation:

The only solution is x = 0

Find the value of x. Please help!!!!

Answers

Answer:

Step-by-step explanation:

In a ∆, equal sides make equal angle to the third side. So the angle that's not mentioned is same '2'.

Sum of angles in a ∆ = 180°

80° + m/_2 + m/_2 = 180°

80° + (5x + 5) + (5x + 5) = 180°

10x + 90° = 180°

10x = 90°

x = 9°

Need this ASAP with the work

Answers

Answer:

Step-by-step explanation:

x/2-5=x/4 +2

x/2-x/4=2+5

x*4-x*2/8=7

4x-2x=8*7

2x=56

x=56/2

x=28

Answer:

J

Step-by-step explanation:

Automatically 1 and 8 are removed as answers since they are too small and go into the negatives, making the other side impossible to be equal. Then just substitute with -20 and 28 and to see which is correct.

Other Questions
Give two examples of each of the following:1.) Physical systems designed by people.2.) Naturally occurring physical systems. 3.) Social systems that you are a part of.4.) Naturally occurring social system. What is the Devils rocks ? Find the value of x. Round to the nearest degree. Hi I need help with this please help me A Carnot engine with an efficiency of 30% operates with a high-temperature reservoir at 188oC and exhausts 2000 J of heat each cycle. What are (a) the heat input per cycle and (b) the Celcius temperature of the low-temperature reservoir Assume a mats price from the start is "X" USD. Write an expression for what the mat would cost after being reduced by P % (unknown amount of percentage) Review the table showing the percentage ofcontaminants remaining in a water sample afterpassing through each round of filters.In the exponential regression equation, what does thevalue of b indicate?Round% of ContaminantsLeft in Water Sample01006.3% of the contaminants remain in the watersample after each round of filters.14.9% of the contaminants remain in the watersample after each round of filters.O 6.3% of the remaining contaminants are removedfrom the water sample after each round of filters.14.9% of the remaining contaminants are removedfrom the water sample after each round of filters.1152230.3 4.The expression for the area of a rectangle whose Length(2p + 4) units and breadth 6 units is:A. 12 + 24pB. 24 + 12pC. 4p + 20D. None of these Write three facts about your animal that you admire: (I'M TIMED) According to the dictionary, -ment can refer to an action, a place, or a state resulting from an action. This definition is useful to know because -ment functions as aA. suffix.B. verb.C. prefix.D. root. Evaluate the algebraic expression h + h when b = 3, d = 12, h = 2 and r = 7. A. 12 B. 8 C. 4 D. 0 When should you paraphrase the ideas in a source rather than using a direct quote?when you want to maintain your own voicewhen the quote is so good it would make your ideas look weakwhen the original quote is not long enoughwhen the quote is includes unrelated information Vista Company installed a standard cost system on January 1. Selected transactions for the month of January are as follows. 1. Purchased 18,400 units of raw materials on account at a cost of $3.90 per unit. Standard cost was $3.80 per unit. 2. Issued 18,400 units of raw materials for jobs that required 18,100 standard units of raw materials. 3. Incurred 16,000 actual hours of direct labor at an actual rate of $4.10 per hour. The standard rate is $4.60 per hour. (Credit Factory Wages Payable). 4. Performed 16,000 hours of direct labor on jobs when standard hours were 16,190. 5. Applied overhead to jobs at the rate of 100% of direct labor cost for standard hours allowed.Journalize the January transactions. Frederick Douglass says that woman is "herself," andthat is the basis of the suffrage movement. Whichstatement would best support his point of view?Read the passage carefully.The fundamental proposition of the woman suffragemovement is scarcely less simple than that of the anti-slavery movement. It assumes that woman is herself.That she belongs to herself, just as fully as man belongsto himself-that she is a person and has all the attributesof personality that can be claimed by man, and that herrights of person are equal in all respects to those of man.She has the same number of senses that distinguish man,and is like man a subject of human government, capableof understanding, obeying and being affected by law.-Speech on the emancipation of women,Frederick DouglassWomen have fewer rights than men.Men are more likely than women to obey laws.Both women and men are capable of many things.Unlike men, women are unable to understand thelaws.Answer C advestsementWhat We have been greatly pleased atYou8 Success. C change the sentencewinit's nown foom of the under lined word) entique se comio 2/5 partes del contenido total de un fravo de conserba de durazno si consumio 16 piesa que cantidad de duraznos haba en el frasc Solve the right triangle. Round decimal answers to the nearest tenth. PLS HELP WILL GIVE BRAINLIEST( IN PIC) PLZ HELPPPPPP!!!!!!!!! I WILL GIVE BRAINLIEST PLEASE