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lorasvet [3.4K]
3 years ago
7

Help me please thank you

Mathematics
1 answer:
lubasha [3.4K]3 years ago
6 0
D..............................
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Let​ T: set of real numbers R Superscript nℝnright arrow→set of real numbers R Superscript mℝm be a linear​ transformation, and
Klio2033 [76]

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.

6 0
3 years ago
A Family spends 240.00 per week on food. If this is 16% of their income, what is the families weekly income?
nexus9112 [7]
Answer: The family's weekly income is $1500

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

Work Shown:

x = weekly income (in dollars)

16% of x = amount spent on food per week
16% of x = 240
(16/100)*x = 240
0.16*x = 240
0.16*x/0.16 = 240/0.16
x = 1500

5 0
3 years ago
3.) in a video game for every 6 enemies
RoseWind [281]
15 points

32/6=5 1/3
if you assume that you only get points after defeating six enemies, you can disregard the 1/3

5*3=15
4 0
3 years ago
Solve each system of equations by graphing y=2/3x+3 3y=2x+15
dangina [55]

Answer:

There is no solution to that equation.

Step-by-step explanation:

First thing to do is to put the second equation in terms of y. To do so the equation becomes y= 2/3x+5. Comparing those two equation you can see that the slopes are the same and thus means that the system has no solution.

Another way to see this is by graphing both of thee equations is a calculator and seeing there are no points of intersection.

7 0
3 years ago
Solve for x: |1/3-x/4|=7/12
ozzi

Your answer is x={-1, 11/3}

4 0
3 years ago
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