Span of two vectorsShowing vectors span a vector space by definitionHow do I determine the intersection of span A and span B?span between vector and set of vectorsSuppose that $v_1,v_2,v_3,v_4$ spans $V$. Prove that the list $v_1 - v_2, v_2 - v_3, v_3-v_4,v_4$ also spans $V$.Is showing that if two vectors in $mathbbR^n$ are linearly independent, then they span $mathbbR^n$?Prove linear independence of two general set of vectorsHelp with proof of two spanning sets of the same spacelinear algebra span of four unknown vectors.Span of two vectors - confusionWhich rows of vectors are linearly dependent or linearly independent?
Perform and show arithmetic with LuaLaTeX
Can an x86 CPU running in real mode be considered to be basically an 8086 CPU?
How old can references or sources in a thesis be?
dbcc cleantable batch size explanation
What's the point of deactivating Num Lock on login screens?
Accidentally leaked the solution to an assignment, what to do now? (I'm the prof)
Can you really stack all of this on an Opportunity Attack?
How does quantile regression compare to logistic regression with the variable split at the quantile?
Cross compiling for RPi - error while loading shared libraries
Can a vampire attack twice with their claws using Multiattack?
What defenses are there against being summoned by the Gate spell?
Does an object always see its latest internal state irrespective of thread?
Revoked SSL certificate
What would happen to a modern skyscraper if it rains micro blackholes?
Watching something be written to a file live with tail
Theorems that impeded progress
Is it unprofessional to ask if a job posting on GlassDoor is real?
Languages that we cannot (dis)prove to be Context-Free
What is a clear way to write a bar that has an extra beat?
Why "Having chlorophyll without photosynthesis is actually very dangerous" and "like living with a bomb"?
Horror movie about a virus at the prom; beginning and end are stylized as a cartoon
I'm flying to France today and my passport expires in less than 2 months
What does the "remote control" for a QF-4 look like?
Roll the carpet
Span of two vectors
Showing vectors span a vector space by definitionHow do I determine the intersection of span A and span B?span between vector and set of vectorsSuppose that $v_1,v_2,v_3,v_4$ spans $V$. Prove that the list $v_1 - v_2, v_2 - v_3, v_3-v_4,v_4$ also spans $V$.Is showing that if two vectors in $mathbbR^n$ are linearly independent, then they span $mathbbR^n$?Prove linear independence of two general set of vectorsHelp with proof of two spanning sets of the same spacelinear algebra span of four unknown vectors.Span of two vectors - confusionWhich rows of vectors are linearly dependent or linearly independent?
$begingroup$
Let $v_1 = (1, 1, -1)$ and $v_2 = (-3, 2, -2)$. Which of the following vectors are in $mathrmspan,v_1, v_2$?
(i) $(4, -1, 1)$
(ii) $(7, -3, 3)$
(iii) $(11, -4, 4)$
I tried to solve for the $c_1,c_2$ but I am really confused and only have 1 answer left, can someone please help???
linear-algebra
edited Mar 21 at 18:04
Brian
1,268216
asked Mar 21 at 17:59
McAMcA
1
$endgroup$
add a comment |
$begingroup$
Let $v_1 = (1, 1, -1)$ and $v_2 = (-3, 2, -2)$. Which of the following vectors are in $mathrmspan,v_1, v_2$?
(i) $(4, -1, 1)$
(ii) $(7, -3, 3)$
(iii) $(11, -4, 4)$
I tried to solve for the $c_1,c_2$ but I am really confused and only have 1 answer left, can someone please help???
linear-algebra
edited Mar 21 at 18:04
Brian
1,268216
asked Mar 21 at 17:59
McAMcA
1
$endgroup$
5
$begingroup$
You have three equations with two unknowns. Do you see these equations? If so, solve for the unknowns using two of the equations. And then plug those values into the third equation. If the answer is consistent, then the vector is in the span. If it is not, then the vector is not in the span.
$endgroup$
– NicNic8
Mar 21 at 18:03
$begingroup$
I don't know what you mean by equations. I created a matrix and tried to solve for c1 and c2
$endgroup$
– McA
Mar 21 at 18:08
$begingroup$
Perhaps, then, you’d care to show us exactly what you mean by “I tried to solve for the $c_1$, $c_2$...”
$endgroup$
– amd
Mar 21 at 18:10
$begingroup$
that's the thing, I checked other solutions and they had v3 but I don't
$endgroup$
– McA
Mar 21 at 18:22
add a comment |
$begingroup$
Let $v_1 = (1, 1, -1)$ and $v_2 = (-3, 2, -2)$. Which of the following vectors are in $mathrmspan,v_1, v_2$?
(i) $(4, -1, 1)$
(ii) $(7, -3, 3)$
(iii) $(11, -4, 4)$
I tried to solve for the $c_1,c_2$ but I am really confused and only have 1 answer left, can someone please help???
linear-algebra
edited Mar 21 at 18:04
Brian
1,268216
asked Mar 21 at 17:59
McAMcA
1
$endgroup$
Let $v_1 = (1, 1, -1)$ and $v_2 = (-3, 2, -2)$. Which of the following vectors are in $mathrmspan,v_1, v_2$?
(i) $(4, -1, 1)$
(ii) $(7, -3, 3)$
(iii) $(11, -4, 4)$
I tried to solve for the $c_1,c_2$ but I am really confused and only have 1 answer left, can someone please help???
linear-algebra
linear-algebra
edited Mar 21 at 18:04
Brian
1,268216
asked Mar 21 at 17:59
McAMcA
1
edited Mar 21 at 18:04
Brian
1,268216
asked Mar 21 at 17:59
McAMcA
1
edited Mar 21 at 18:04
Brian
1,268216
edited Mar 21 at 18:04
Brian
1,268216
edited Mar 21 at 18:04
Brian
1,268216
1,268216
asked Mar 21 at 17:59
McAMcA
1
asked Mar 21 at 17:59
McAMcA
1
asked Mar 21 at 17:59
McAMcA
1
1
5
$begingroup$
You have three equations with two unknowns. Do you see these equations? If so, solve for the unknowns using two of the equations. And then plug those values into the third equation. If the answer is consistent, then the vector is in the span. If it is not, then the vector is not in the span.
$endgroup$
– NicNic8
Mar 21 at 18:03
$begingroup$
I don't know what you mean by equations. I created a matrix and tried to solve for c1 and c2
$endgroup$
– McA
Mar 21 at 18:08
$begingroup$
Perhaps, then, you’d care to show us exactly what you mean by “I tried to solve for the $c_1$, $c_2$...”
$endgroup$
– amd
Mar 21 at 18:10
$begingroup$
that's the thing, I checked other solutions and they had v3 but I don't
$endgroup$
– McA
Mar 21 at 18:22
add a comment |
5
$begingroup$
You have three equations with two unknowns. Do you see these equations? If so, solve for the unknowns using two of the equations. And then plug those values into the third equation. If the answer is consistent, then the vector is in the span. If it is not, then the vector is not in the span.
$endgroup$
– NicNic8
Mar 21 at 18:03
$begingroup$
I don't know what you mean by equations. I created a matrix and tried to solve for c1 and c2
$endgroup$
– McA
Mar 21 at 18:08
$begingroup$
Perhaps, then, you’d care to show us exactly what you mean by “I tried to solve for the $c_1$, $c_2$...”
$endgroup$
– amd
Mar 21 at 18:10
$begingroup$
that's the thing, I checked other solutions and they had v3 but I don't
$endgroup$
– McA
Mar 21 at 18:22
5
5
$begingroup$
You have three equations with two unknowns. Do you see these equations? If so, solve for the unknowns using two of the equations. And then plug those values into the third equation. If the answer is consistent, then the vector is in the span. If it is not, then the vector is not in the span.
$endgroup$
– NicNic8
Mar 21 at 18:03
$begingroup$
You have three equations with two unknowns. Do you see these equations? If so, solve for the unknowns using two of the equations. And then plug those values into the third equation. If the answer is consistent, then the vector is in the span. If it is not, then the vector is not in the span.
$endgroup$
– NicNic8
Mar 21 at 18:03
$begingroup$
I don't know what you mean by equations. I created a matrix and tried to solve for c1 and c2
$endgroup$
– McA
Mar 21 at 18:08
$begingroup$
I don't know what you mean by equations. I created a matrix and tried to solve for c1 and c2
$endgroup$
– McA
Mar 21 at 18:08
$begingroup$
Perhaps, then, you’d care to show us exactly what you mean by “I tried to solve for the $c_1$, $c_2$...”
$endgroup$
– amd
Mar 21 at 18:10
$begingroup$
Perhaps, then, you’d care to show us exactly what you mean by “I tried to solve for the $c_1$, $c_2$...”
$endgroup$
– amd
Mar 21 at 18:10
$begingroup$
that's the thing, I checked other solutions and they had v3 but I don't
$endgroup$
– McA
Mar 21 at 18:22
$begingroup$
that's the thing, I checked other solutions and they had v3 but I don't
$endgroup$
– McA
Mar 21 at 18:22
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Calculate $v_1-v_2$, $v_1-2c_2$ and $2v_1-3c_2$.
In case you've found that vector (i) and vector (ii) are in the span, save some work by observing that vector (iii) is the sum of both.
answered Mar 21 at 18:42
Michael HoppeMichael Hoppe
11.3k31837
$endgroup$
$begingroup$
thanks a lot!!!
$endgroup$
– McA
Mar 21 at 18:51
add a comment |
$begingroup$
We can somewhat 'simplify' the basis vectors by noting that the span of $v_1,v_2$ is also the span of $dfrac2v_1-v_25,dfrac3v_1+v_25equiv(1,0,0),(0,1,-1)$. Now it's easy to see which vectors lie in the span.
answered Mar 21 at 18:52
Shubham JohriShubham Johri
5,500818
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
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
);
);
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
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3157156%2fspan-of-two-vectors%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Calculate $v_1-v_2$, $v_1-2c_2$ and $2v_1-3c_2$.
In case you've found that vector (i) and vector (ii) are in the span, save some work by observing that vector (iii) is the sum of both.
answered Mar 21 at 18:42
Michael HoppeMichael Hoppe
11.3k31837
$endgroup$
$begingroup$
thanks a lot!!!
$endgroup$
– McA
Mar 21 at 18:51
add a comment |
$begingroup$
Calculate $v_1-v_2$, $v_1-2c_2$ and $2v_1-3c_2$.
In case you've found that vector (i) and vector (ii) are in the span, save some work by observing that vector (iii) is the sum of both.
answered Mar 21 at 18:42
Michael HoppeMichael Hoppe
11.3k31837
$endgroup$
$begingroup$
thanks a lot!!!
$endgroup$
– McA
Mar 21 at 18:51
add a comment |
$begingroup$
Calculate $v_1-v_2$, $v_1-2c_2$ and $2v_1-3c_2$.
In case you've found that vector (i) and vector (ii) are in the span, save some work by observing that vector (iii) is the sum of both.
answered Mar 21 at 18:42
Michael HoppeMichael Hoppe
11.3k31837
$endgroup$
Calculate $v_1-v_2$, $v_1-2c_2$ and $2v_1-3c_2$.
In case you've found that vector (i) and vector (ii) are in the span, save some work by observing that vector (iii) is the sum of both.
answered Mar 21 at 18:42
Michael HoppeMichael Hoppe
11.3k31837
answered Mar 21 at 18:42
Michael HoppeMichael Hoppe
11.3k31837
answered Mar 21 at 18:42
Michael HoppeMichael Hoppe
11.3k31837
answered Mar 21 at 18:42
Michael HoppeMichael Hoppe
11.3k31837
11.3k31837
$begingroup$
thanks a lot!!!
$endgroup$
– McA
Mar 21 at 18:51
add a comment |
$begingroup$
thanks a lot!!!
$endgroup$
– McA
Mar 21 at 18:51
$begingroup$
thanks a lot!!!
$endgroup$
– McA
Mar 21 at 18:51
$begingroup$
thanks a lot!!!
$endgroup$
– McA
Mar 21 at 18:51
add a comment |
$begingroup$
We can somewhat 'simplify' the basis vectors by noting that the span of $v_1,v_2$ is also the span of $dfrac2v_1-v_25,dfrac3v_1+v_25equiv(1,0,0),(0,1,-1)$. Now it's easy to see which vectors lie in the span.
answered Mar 21 at 18:52
Shubham JohriShubham Johri
5,500818
$endgroup$
add a comment |
$begingroup$
We can somewhat 'simplify' the basis vectors by noting that the span of $v_1,v_2$ is also the span of $dfrac2v_1-v_25,dfrac3v_1+v_25equiv(1,0,0),(0,1,-1)$. Now it's easy to see which vectors lie in the span.
answered Mar 21 at 18:52
Shubham JohriShubham Johri
5,500818
$endgroup$
add a comment |
$begingroup$
We can somewhat 'simplify' the basis vectors by noting that the span of $v_1,v_2$ is also the span of $dfrac2v_1-v_25,dfrac3v_1+v_25equiv(1,0,0),(0,1,-1)$. Now it's easy to see which vectors lie in the span.
answered Mar 21 at 18:52
Shubham JohriShubham Johri
5,500818
$endgroup$
We can somewhat 'simplify' the basis vectors by noting that the span of $v_1,v_2$ is also the span of $dfrac2v_1-v_25,dfrac3v_1+v_25equiv(1,0,0),(0,1,-1)$. Now it's easy to see which vectors lie in the span.
answered Mar 21 at 18:52
Shubham JohriShubham Johri
5,500818
answered Mar 21 at 18:52
Shubham JohriShubham Johri
5,500818
answered Mar 21 at 18:52
Shubham JohriShubham Johri
5,500818
answered Mar 21 at 18:52
Shubham JohriShubham Johri
5,500818
5,500818
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
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
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3157156%2fspan-of-two-vectors%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
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
Required, but never shown
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
Required, but never shown
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
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
5
$begingroup$
You have three equations with two unknowns. Do you see these equations? If so, solve for the unknowns using two of the equations. And then plug those values into the third equation. If the answer is consistent, then the vector is in the span. If it is not, then the vector is not in the span.
$endgroup$
– NicNic8
Mar 21 at 18:03
$begingroup$
I don't know what you mean by equations. I created a matrix and tried to solve for c1 and c2
$endgroup$
– McA
Mar 21 at 18:08
$begingroup$
Perhaps, then, you’d care to show us exactly what you mean by “I tried to solve for the $c_1$, $c_2$...”
$endgroup$
– amd
Mar 21 at 18:10
$begingroup$
that's the thing, I checked other solutions and they had v3 but I don't
$endgroup$
– McA
Mar 21 at 18:22