Fdtxjr

Using audio cues to encourage good posture

Converted a Scalar function to a TVF function for parallel execution-Still running in Serial mode

How does the math work when buying airline miles?

A term for a woman complaining about things/begging in a cute/childish way

What is "gratricide"?

Crossing US/Canada Border for less than 24 hours

How come Sam didn't become Lord of Horn Hill?

Why is Nikon 1.4g better when Nikon 1.8g is sharper?

Is it possible for SQL statements to execute concurrently within a single session in SQL Server?

Disembodied hand growing fangs

Illegal assignment from sObject to Id

What is the meaning of 'breadth' in breadth first search?

Time to Settle Down!

How does Python know the values already stored in its memory?

Taylor expansion of ln(1-x)

Is there any word for a place full of confusion?

An adverb for when you're not exaggerating

Why weren't discrete x86 CPUs ever used in game hardware?

Is it a good idea to use CNN to classify 1D signal?

Is it fair for a professor to grade us on the possession of past papers?

Find 108 by using 3,4,6

Can a new player join a group only when a new campaign starts?

How do living politicians protect their readily obtainable signatures from misuse?

If Windows 7 doesn't support WSL, then what does Linux subsystem option mean?

write coordinates in the base of $1,x,x^2,x^3$

0

1

$begingroup$

I am given this task and have no clue what to do.

We are given, linear space,which is spanned by polynomials (with real coefficients), whose degrees are at most 3, and we are give the polynomial $f(x) =2-3x+x^3$

How can I write $f(x)$ coordinates in the base $1,x,x^2,x^3$?

linear-algebra

share|cite|improve this question

edited Mar 27 at 17:48

Shubham Johri

5,668918

asked Mar 27 at 17:45

EdvardsZEdvardsZ

31

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Can you write $2-3x+x^3$ as a linear combination of $1, x, x^2, x^3$?
  $endgroup$
  – J. W. Tanner
  Mar 27 at 17:51
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to the website. Refer here for a quick guide on Mathjax to typeset your Math equations in the future.
  $endgroup$
  – Shubham Johri
  Mar 27 at 17:53
  

  
  
  
  

add a comment | 

0

1

$begingroup$

I am given this task and have no clue what to do.

We are given, linear space,which is spanned by polynomials (with real coefficients), whose degrees are at most 3, and we are give the polynomial $f(x) =2-3x+x^3$

How can I write $f(x)$ coordinates in the base $1,x,x^2,x^3$?

linear-algebra

share|cite|improve this question

edited Mar 27 at 17:48

Shubham Johri

5,668918

asked Mar 27 at 17:45

EdvardsZEdvardsZ

31

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Can you write $2-3x+x^3$ as a linear combination of $1, x, x^2, x^3$?
  $endgroup$
  – J. W. Tanner
  Mar 27 at 17:51
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to the website. Refer here for a quick guide on Mathjax to typeset your Math equations in the future.
  $endgroup$
  – Shubham Johri
  Mar 27 at 17:53
  

  
  
  
  

add a comment | 

$begingroup$

I am given this task and have no clue what to do.

We are given, linear space,which is spanned by polynomials (with real coefficients), whose degrees are at most 3, and we are give the polynomial $f(x) =2-3x+x^3$

How can I write $f(x)$ coordinates in the base $1,x,x^2,x^3$?

linear-algebra

share|cite|improve this question

edited Mar 27 at 17:48

Shubham Johri

5,668918

asked Mar 27 at 17:45

EdvardsZEdvardsZ

31

$endgroup$

share|cite|improve this question

edited Mar 27 at 17:48

Shubham Johri

5,668918

asked Mar 27 at 17:45

EdvardsZEdvardsZ

31

share|cite|improve this question

edited Mar 27 at 17:48

Shubham Johri

5,668918

asked Mar 27 at 17:45

EdvardsZEdvardsZ

31

edited Mar 27 at 17:48

Shubham Johri

5,668918

edited Mar 27 at 17:48

Shubham Johri

5,668918

asked Mar 27 at 17:45

EdvardsZEdvardsZ

31

asked Mar 27 at 17:45

EdvardsZEdvardsZ

31

2 Answers
2

active

oldest

votes

0

$begingroup$

When in doubt, go back to basic definitions. What does it mean for the tuple $(a,b,c,d)$ to be the coordinates of a vector $mathbf v$ relative to some ordered basis $mathcal B=(mathbf v_1, mathbf v_2,mathbf v_3,mathbf v_4)$? It means that $mathbf v$ can be expressed uniquely as the linear combination $amathbf v_1+bmathbf v_2+cmathbf v_3+dmathbf v_4$, i.e., the coordinates of $mathbf v$ relative to $mathcal B$ are exactly the coefficients of the basis vectors in that unique linear combination.

Knowing this, what do you think the coordinates of the polynomial $a+bx+cx^2+dx^3$ relative to the ordered basis $(1,x,x^2,x^3)$ are?

share|cite|improve this answer

answered Mar 27 at 18:29

amdamd

31.9k21053

$endgroup$

add a comment | 

0

$begingroup$

Hint

Let the co-ordinates of $f(x)$ with respect to the (ordered) basis $1,x,x^2,x^3$ be $(a,b,c,d)$. This means $f(x)=2-3x+x^3=a+bx+cx^2+dx^3$. Now compare the coefficients of different powers of $x$ on each side.

share|cite|improve this answer

answered Mar 27 at 17:51

Shubham JohriShubham Johri

5,668918

$endgroup$

add a comment | 

Your Answer

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name

Email

Required, but never shown

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3164844%2fwrite-coordinates-in-the-base-of-1-x-x2-x3%23new-answer', 'question_page');

);

Post as a guest

Name

Email

Required, but never shown

0

$begingroup$

When in doubt, go back to basic definitions. What does it mean for the tuple $(a,b,c,d)$ to be the coordinates of a vector $mathbf v$ relative to some ordered basis $mathcal B=(mathbf v_1, mathbf v_2,mathbf v_3,mathbf v_4)$? It means that $mathbf v$ can be expressed uniquely as the linear combination $amathbf v_1+bmathbf v_2+cmathbf v_3+dmathbf v_4$, i.e., the coordinates of $mathbf v$ relative to $mathcal B$ are exactly the coefficients of the basis vectors in that unique linear combination.

Knowing this, what do you think the coordinates of the polynomial $a+bx+cx^2+dx^3$ relative to the ordered basis $(1,x,x^2,x^3)$ are?

share|cite|improve this answer

answered Mar 27 at 18:29

amdamd

31.9k21053

$endgroup$

add a comment | 

0

$begingroup$

When in doubt, go back to basic definitions. What does it mean for the tuple $(a,b,c,d)$ to be the coordinates of a vector $mathbf v$ relative to some ordered basis $mathcal B=(mathbf v_1, mathbf v_2,mathbf v_3,mathbf v_4)$? It means that $mathbf v$ can be expressed uniquely as the linear combination $amathbf v_1+bmathbf v_2+cmathbf v_3+dmathbf v_4$, i.e., the coordinates of $mathbf v$ relative to $mathcal B$ are exactly the coefficients of the basis vectors in that unique linear combination.

Knowing this, what do you think the coordinates of the polynomial $a+bx+cx^2+dx^3$ relative to the ordered basis $(1,x,x^2,x^3)$ are?

share|cite|improve this answer

answered Mar 27 at 18:29

amdamd

31.9k21053

$endgroup$

add a comment | 

$begingroup$

When in doubt, go back to basic definitions. What does it mean for the tuple $(a,b,c,d)$ to be the coordinates of a vector $mathbf v$ relative to some ordered basis $mathcal B=(mathbf v_1, mathbf v_2,mathbf v_3,mathbf v_4)$? It means that $mathbf v$ can be expressed uniquely as the linear combination $amathbf v_1+bmathbf v_2+cmathbf v_3+dmathbf v_4$, i.e., the coordinates of $mathbf v$ relative to $mathcal B$ are exactly the coefficients of the basis vectors in that unique linear combination.

Knowing this, what do you think the coordinates of the polynomial $a+bx+cx^2+dx^3$ relative to the ordered basis $(1,x,x^2,x^3)$ are?

share|cite|improve this answer

answered Mar 27 at 18:29

amdamd

31.9k21053

$endgroup$

share|cite|improve this answer

answered Mar 27 at 18:29

amdamd

31.9k21053

answered Mar 27 at 18:29

amdamd

31.9k21053

answered Mar 27 at 18:29

amdamd

31.9k21053

0

$begingroup$

Hint

Let the co-ordinates of $f(x)$ with respect to the (ordered) basis $1,x,x^2,x^3$ be $(a,b,c,d)$. This means $f(x)=2-3x+x^3=a+bx+cx^2+dx^3$. Now compare the coefficients of different powers of $x$ on each side.

share|cite|improve this answer

answered Mar 27 at 17:51

Shubham JohriShubham Johri

5,668918

$endgroup$

add a comment | 

0

$begingroup$

Hint

Let the co-ordinates of $f(x)$ with respect to the (ordered) basis $1,x,x^2,x^3$ be $(a,b,c,d)$. This means $f(x)=2-3x+x^3=a+bx+cx^2+dx^3$. Now compare the coefficients of different powers of $x$ on each side.

share|cite|improve this answer

answered Mar 27 at 17:51

Shubham JohriShubham Johri

5,668918

$endgroup$

add a comment | 

$begingroup$

Hint

Let the co-ordinates of $f(x)$ with respect to the (ordered) basis $1,x,x^2,x^3$ be $(a,b,c,d)$. This means $f(x)=2-3x+x^3=a+bx+cx^2+dx^3$. Now compare the coefficients of different powers of $x$ on each side.

share|cite|improve this answer

answered Mar 27 at 17:51

Shubham JohriShubham Johri

5,668918

$endgroup$

share|cite|improve this answer

answered Mar 27 at 17:51

Shubham JohriShubham Johri

5,668918

answered Mar 27 at 17:51

Shubham JohriShubham Johri

5,668918

answered Mar 27 at 17:51

Shubham JohriShubham Johri

5,668918