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
9966 [12]
3 years ago
14

Let​ T: set of real numbers R Superscript nℝnright arrow→set of real numbers R Superscript mℝm be a linear​ transformation, and

let ​{v1​, v2​, v3​} be a linearly dependent set in set of real numbers R Superscript nℝn. Explain why the set ​{T(v1​), ​T(v2​), ​T(v3​)} is linearly dependent.
Mathematics
1 answer:
Klio2033 [76]3 years ago
6 0

Answer:

\{T(v_1), T(v_2), T(v_3)\} is linearly dependent set.

Step-by-step explanation:

Given:  \{v_1,v_2,v_3\} is a linearly dependent set in set of real numbers R

To show: the set \{T(v_1), T(v_2), T(v_3)\} is linearly dependent.

Solution:

If \{v_1,v_2,v_3,...,v_n\} is a set of linearly dependent vectors then there exists atleast one k_i:i=1,2,3,...,n such that k_1v_1+k_2v_2+k_3v_3+...+k_nv_n=0

Consider k_1T(v_1)+k_2T(v_2)+k_3T(v_3)=0

A linear transformation T: U→V satisfies the following properties:

1. T(u_1+u_2)=T(u_1)+T(u_2)

2. T(au)=aT(u)

Here, u,u_1,u_2∈ U

As T is a linear transformation,

k_1T(v_1)+k_2T(v_2)+k_3T(v_3)=0\\T(k_1v_1)+T(k_2v_2)+T(k_3v_3)=0\\T(k_1v_1+k_2v_2+k_3v_3)=0\\

As \{v_1,v_2,v_3\} is a linearly dependent set,

k_1v_1+k_2v_2+k_3v_3=0 for some k_i\neq 0:i=1,2,3

So, for some k_i\neq 0:i=1,2,3

k_1T(v_1)+k_2T(v_2)+k_3T(v_3)=0

Therefore, set \{T(v_1), T(v_2), T(v_3)\} is linearly dependent.

You might be interested in
HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Bezzdna [24]
The answer is option C. 9xy sqrt 2x
5 0
3 years ago
A ball is thrown upward from ground level. Its height h, in feet, above the ground after t seconds is h-48t -16t^2.
Marat540 [252]

Answer:

36 feet.

Step-by-step explanation:

We have been given that a ball is thrown upward from ground level. Its height h, in feet, above the ground after t seconds is h(t)=-48t -16t^2. We are asked to find the maximum height of the ball.

We can see that our given equation is a downward opening parabola, so its maximum height will be the vertex of the parabola.

To find the maximum height of the ball, we need to find y-coordinate of vertex of parabola.

Let us find x-coordinate of parabola using formula x=-\frac{b}{2a}.

x=-\frac{-48}{2(-16)}

x=-\frac{48}{32}

x=-\frac{3}{2}

So, the x-coordinate of the parabola is -\frac{3}{2}. Now, we will substitute x=-\frac{3}{2} in our given equation to find y-coordinate of parabola.

h(t)=-48t -16t^2

h(-\frac{3}{2})=-48(-\frac{3}{2})-16(-\frac{3}{2})^2

h(-\frac{3}{2})=-24(-3)-16(\frac{9}{4})

h(-\frac{3}{2})=72-4*9

h(-\frac{3}{2})=72-36

h(-\frac{3}{2})=36

Therefore, the maximum height of the ball is 36 feet.

3 0
3 years ago
Find the area of this shape.
ch4aika [34]
The top part of the shape is 8x6 and the bottom part is 6x6 so the answer is 84
3 0
3 years ago
I cant get this one, 216−(−83)+(−479)
Inessa [10]

Answer:

180

Step-by-step explanation:

=216-(-83)+(-479)

=216+83-479

=299-479

=180

7 0
3 years ago
In 15 years lisa will be four times as old as she is now. how old is she now
Eva8 [605]

Answer:

Lisa is 5 years old

Step-by-step explanation:

we can make an equation like

4x=15+x

X can represent Lisa’s current age

Now just solve for X

3x=15

x=5

And we can check

If Lisa is 5 years old now

In 15 years she would be 20

And 20 is 4 times as 5 which Is her current age

So Lisa is 5 years old now.

5 0
3 years ago
Other questions:
  • Marcus Butler book of tickets to use at the amusement park has 50% of the tickets on rides one third of the tickets on video gam
    6·1 answer
  • The temperature in several cities in Canada are shown in the table to the right. The average temperature can be found in the sum
    9·1 answer
  • The population of a city is 250,000 and the annual growth rate is 2.2%. Write an equation to model the population y after x year
    14·1 answer
  • In baseball, the equation E = 9RI gives a pitcher's earned run average, E where R is the number of earned runs the player is all
    14·1 answer
  • If the Cost price of the an article is greater than the selling price, we have a ____?​
    7·1 answer
  • X: ax squared = bx? can someone help me
    14·1 answer
  • In the diagram shown, line m is parallel to line n. Cruz says that ∠4 and ∠6 are congruent angles. Is he correct? Why or why not
    10·2 answers
  • An article in IEEE International Symposium on Electromagnetic Compatibility (Vol. 2, 2002, pp. 667-670) describes the quantifica
    14·1 answer
  • Find the exact value of each expression.<br> sin75°<br> cos(-75°)
    8·2 answers
  • (50 points really need help on this it's the last question)
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!