1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
jasenka [17]
2 years ago
5

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

Mathematics
1 answer:
erastovalidia [21]2 years ago
4 0

Let <em>u</em> = (1, 0) and <em>v</em> = (0, 1). Then

<em>T</em> (<em>u</em>) = (2*1 - 3*0, 1 + 4, 5*0) = (2, 5, 0)

<em>T</em> (<em>v</em>) = (2*0 - 3*1, 0 + 4, 5*1) = (-3, 4, 5)

=>   <em>T</em> (<em>u</em>) + <em>T</em> (<em>v</em>) = (-1, 9, 5)

but

<em>T</em> (<em>u</em> + <em>v</em>) = <em>T</em> (1, 1) = (2*1 - 3*1, 1 + 4, 5*1) = (-1, 5, 5)

=>   <em>T</em> (<em>u</em> + <em>v</em>) ≠ <em>T</em> (<em>u</em>) + <em>T</em> (<em>v</em>)

which means <em>T</em> does not preserve addition, so it is not linear.

You might be interested in
Oshua's mother has a family Christmas gathering at 2:00. Joshua must travel 348 miles to join the festivities. He left his house
gavmur [86]

Answer:

58 miles/hour

Step-by-step explanation:

Given that the family Christmas gathering has been scheduled at 2:00 p.m.,

and Joshua left the house at 8:00 a.m.

So, the total time available in order to arrive on time to attend the Christmas gathering, t=6 hours

The total distance, Joshua has to travel, d= 348 miles.

As average speed= (total distance)/(total time)

So, the average speed of driving = 348/6=58 miles/hour

Hence, Joshua must drive at an average speed of 58 miles/hour in order to arrive on time.

7 0
2 years ago
Round 607.5 to the nearest whole number.
kari74 [83]
608

607.5

.5 rounds up to 1

607+1=608
7 0
2 years ago
Read 2 more answers
Help for brainliest please
tiny-mole [99]

Answer:

yes I know the answer.com

4 0
2 years ago
Read 2 more answers
The equation of a vertical line has what format
saveliy_v [14]
X=_________
or 
y=_________
Most likely it will be x=s.
7 0
3 years ago
What are the solutions to the following system? StartLayout Enlarged left-brace 1st row negative 2 x squared + y = negative 5 2n
Yakvenalex [24]

Answer:

(\sqrt{2},-1),(-\sqrt{2},-1)

(StartRoot 2 EndRoot, negative 1) and (negative StartRoot 2 EndRoot, negative 1)

Step-by-step explanation:

we have

-2x^{2} +y=-5 ----> equation A

y=-3x^{2} +5 -----> equation B

solve by substitution

substitute equation B in equation A

-2x^{2} +(-3x^{2} +5)=-5

solve for x

-5x^{2} +5=-5

-5x^{2}=-10

x^{2}=2

x=\pm\sqrt{2}

<em>Find the value of y</em>

y=-3x^{2} +5

For x=\sqrt{2} ----> y=-3(\sqrt{2})^{2} +5=-1

For x=-\sqrt{2} ----> y=-3(-\sqrt{2})^{2} +5=-1

therefore

The solutions are

(\sqrt{2},-1),(-\sqrt{2},-1)

(StartRoot 2 EndRoot, negative 1) and (negative StartRoot 2 EndRoot, negative 1)

8 0
3 years ago
Read 2 more answers
Other questions:
  • a goat tethered to a stake by a rope has grazed the meadow over an area of 12.56msqare around it stretching the rope. i) what is
    12·2 answers
  • Mr. Berger assigned the following system of equations to be solved for homework.
    6·1 answer
  • How many 2/3 are in 8/9​
    9·2 answers
  • Kalvin and 4 of his friends want
    5·2 answers
  • Which direction does the graph of f(x) = −18 + x2 − 3x open?
    7·1 answer
  • Definition: A number greater than 0 is called ____.
    9·2 answers
  • What is the area surface of a cylinder 11x8
    5·1 answer
  • F(x) = 6 x+50<br> Domain and range
    14·1 answer
  • Help me please I'm very confused about this!
    9·1 answer
  • H
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!