Range of linear mapping [closed]

0

$begingroup$

In this example, why is the range given as $Range(L)= (1+x, x)$ and not as simply $(1, x)$.

I thought that it would be $(1,x)$ since we can use a linear combination of $1$ and $x$ to express the form $(a+b) + (a+b+c)x$.

linear-algebra linear-transformations

share|cite|improve this question

edited Jan 2 at 13:21

Jneven

756320

asked Jan 2 at 12:44

P.ythonP.ython

205

$endgroup$

closed as off-topic by Lord Shark the Unknown, Shailesh, KReiser, Paul Frost, user91500 Jan 3 at 12:09

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Lord Shark the Unknown, Shailesh, KReiser, Paul Frost, user91500

If this question can be reworded to fit the rules in the help center, please edit the question.

add a comment | 

0

$begingroup$

In this example, why is the range given as $Range(L)= (1+x, x)$ and not as simply $(1, x)$.

I thought that it would be $(1,x)$ since we can use a linear combination of $1$ and $x$ to express the form $(a+b) + (a+b+c)x$.

linear-algebra linear-transformations

share|cite|improve this question

edited Jan 2 at 13:21

Jneven

756320

asked Jan 2 at 12:44

P.ythonP.ython

205

$endgroup$

closed as off-topic by Lord Shark the Unknown, Shailesh, KReiser, Paul Frost, user91500 Jan 3 at 12:09

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Lord Shark the Unknown, Shailesh, KReiser, Paul Frost, user91500

If this question can be reworded to fit the rules in the help center, please edit the question.

add a comment | 

0

0

0

$begingroup$

In this example, why is the range given as $Range(L)= (1+x, x)$ and not as simply $(1, x)$.

I thought that it would be $(1,x)$ since we can use a linear combination of $1$ and $x$ to express the form $(a+b) + (a+b+c)x$.

linear-algebra linear-transformations

share|cite|improve this question

edited Jan 2 at 13:21

Jneven

756320

asked Jan 2 at 12:44

P.ythonP.ython

205

$endgroup$

In this example, why is the range given as $Range(L)= (1+x, x)$ and not as simply $(1, x)$.

I thought that it would be $(1,x)$ since we can use a linear combination of $1$ and $x$ to express the form $(a+b) + (a+b+c)x$.

linear-algebra linear-transformations

linear-algebra linear-transformations

share|cite|improve this question

edited Jan 2 at 13:21

Jneven

756320

asked Jan 2 at 12:44

P.ythonP.ython

205

share|cite|improve this question

edited Jan 2 at 13:21

Jneven

756320

asked Jan 2 at 12:44

P.ythonP.ython

205

share|cite|improve this question

share|cite|improve this question

edited Jan 2 at 13:21

Jneven

756320

edited Jan 2 at 13:21

Jneven

756320

edited Jan 2 at 13:21

Jneven

756320

756320

asked Jan 2 at 12:44

P.ythonP.ython

205

asked Jan 2 at 12:44

P.ythonP.ython

205

asked Jan 2 at 12:44

P.ythonP.ython

205

205

closed as off-topic by Lord Shark the Unknown, Shailesh, KReiser, Paul Frost, user91500 Jan 3 at 12:09

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Lord Shark the Unknown, Shailesh, KReiser, Paul Frost, user91500

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by Lord Shark the Unknown, Shailesh, KReiser, Paul Frost, user91500 Jan 3 at 12:09

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Lord Shark the Unknown, Shailesh, KReiser, Paul Frost, user91500

If this question can be reworded to fit the rules in the help center, please edit the question.

add a comment | 

add a comment | 

1 Answer
1

active

oldest

votes

2

$begingroup$

Is $P_1$ the set of polynomials of degree $leq 1$?

In any case, the span of $(1,x)$ and $(1+x,x)$ is the same. That is to say, any polynomial that you can write as a linear combination of $1$ and $x$ you can also write as a linear combination of $1+x$ and $x$ and vice versa.

For example, we can write the polynomial $a+bx$ as $a(1+x) + (b-a)x$.

Also, as a side note, it would be better if you used mathjax to type the content from the image, or at least properly cropped the image.

share|cite|improve this answer

answered Jan 2 at 15:22

tchtch

639210

$endgroup$

add a comment | 

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

2

$begingroup$

Is $P_1$ the set of polynomials of degree $leq 1$?

In any case, the span of $(1,x)$ and $(1+x,x)$ is the same. That is to say, any polynomial that you can write as a linear combination of $1$ and $x$ you can also write as a linear combination of $1+x$ and $x$ and vice versa.

For example, we can write the polynomial $a+bx$ as $a(1+x) + (b-a)x$.

Also, as a side note, it would be better if you used mathjax to type the content from the image, or at least properly cropped the image.

share|cite|improve this answer

answered Jan 2 at 15:22

tchtch

639210

$endgroup$

add a comment | 

2

$begingroup$

Is $P_1$ the set of polynomials of degree $leq 1$?

In any case, the span of $(1,x)$ and $(1+x,x)$ is the same. That is to say, any polynomial that you can write as a linear combination of $1$ and $x$ you can also write as a linear combination of $1+x$ and $x$ and vice versa.

For example, we can write the polynomial $a+bx$ as $a(1+x) + (b-a)x$.

Also, as a side note, it would be better if you used mathjax to type the content from the image, or at least properly cropped the image.

share|cite|improve this answer

answered Jan 2 at 15:22

tchtch

639210

$endgroup$

add a comment | 

2

2

2

$begingroup$

Is $P_1$ the set of polynomials of degree $leq 1$?

In any case, the span of $(1,x)$ and $(1+x,x)$ is the same. That is to say, any polynomial that you can write as a linear combination of $1$ and $x$ you can also write as a linear combination of $1+x$ and $x$ and vice versa.

For example, we can write the polynomial $a+bx$ as $a(1+x) + (b-a)x$.

Also, as a side note, it would be better if you used mathjax to type the content from the image, or at least properly cropped the image.

share|cite|improve this answer

answered Jan 2 at 15:22

tchtch

639210

$endgroup$

Is $P_1$ the set of polynomials of degree $leq 1$?

In any case, the span of $(1,x)$ and $(1+x,x)$ is the same. That is to say, any polynomial that you can write as a linear combination of $1$ and $x$ you can also write as a linear combination of $1+x$ and $x$ and vice versa.

For example, we can write the polynomial $a+bx$ as $a(1+x) + (b-a)x$.

Also, as a side note, it would be better if you used mathjax to type the content from the image, or at least properly cropped the image.

share|cite|improve this answer

answered Jan 2 at 15:22

tchtch

639210

share|cite|improve this answer

share|cite|improve this answer

answered Jan 2 at 15:22

tchtch

639210

answered Jan 2 at 15:22

tchtch

639210

answered Jan 2 at 15:22

tchtch

639210

639210

add a comment | 

add a comment | 

This page is only for reference, If you need detailed information, please check here