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Paha777 [63]
3 years ago
7

Is this done correctly??​

Mathematics
1 answer:
Naily [24]3 years ago
8 0

Answer:

YES! That is correct

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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
Round 7.3519 to 1 decimal place
Temka [501]
7.4 is your final answer, hope that help, one decimal place is the first number after the decimal.
8 0
3 years ago
20 pts, try to find short story and novel pages, A novel has 13 times as many pages as a short story. The combined number of pag
brilliants [131]

Answer:

short story has 32 pgs

novel has 416 pgs

Step-by-step explanation:

a novel (N) has 13 times as many pages as a short story (x) so, N = 13X

total pages is the equation N + x = 448

plug the equation for N into this

13x + x = 448, combine like terms

14x = 448, divide both sides by 14

x = 32. so now we know that the short story has 32 pages. subtract that from 448. and the novel has 416 pages.

8 0
2 years ago
sam's music teacher told him to practice his trombone for X amount of hours. he spent X amount of hours practicing did he practi
Crank
Yes if he practices X amount of hours and is told to practice X amount of hours than he practiced long enough
4 0
3 years ago
9.99x10 ^-2 + 1.11 × 10^-2 i dont have the same scientific calculator as the one from school. Would like to verify my math is co
Rufina [12.5K]
The answer should not depend on which machine or which pencil you use to
find it.  If you work a problem two different ways and get two different answers,
then at least one of them is wrong, and there's a pretty good chance that both
of them are.

(9.99 of anything) + (1.11 of the same thing) = 11.1 of them

9.99 (x 10^-2) + 1.11 (x 10^-2) = <em>11.1 (x 10^-2)</em> .

Can we do any more with that ?

10^-2  =  1 / 10^2  =  1 / 100 .

11.1 x 10^-2  =  11.1 / 100  =  <em>0.111</em>
3 0
3 years ago
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