Spanning with Independent and Dependent Vectors
$begingroup$
Given the vectors
v1 = (a,b,c)
v2 = (d,e,f)
v3 = (x,y,z)
Where v1 and v3 are dependent ( I don't know yet ) and I am asked to calculate the span of the vectors, how would I do it?
If I calculate the determinat it will result 0 so it would only prove that it won't span the R^3, but what do I do next to prove if it spans ( or not ) R^2
linear-algebra vector-spaces
asked Dec 2 '18 at 22:05
Calin ChalyCalin Chaly
1
$endgroup$
add a comment |
$begingroup$
Given the vectors
v1 = (a,b,c)
v2 = (d,e,f)
v3 = (x,y,z)
Where v1 and v3 are dependent ( I don't know yet ) and I am asked to calculate the span of the vectors, how would I do it?
If I calculate the determinat it will result 0 so it would only prove that it won't span the R^3, but what do I do next to prove if it spans ( or not ) R^2
linear-algebra vector-spaces
asked Dec 2 '18 at 22:05
Calin ChalyCalin Chaly
1
$endgroup$
$begingroup$
If $v_1$ and $v_3$ are dependant of each other, if one of them is non-zero, $v_1$ say, we know that $v_1 = kcdot v_3$, so span of this $3$ vectors would be span of $v_1$ and $v_2$.
$endgroup$
– Jakobian
Dec 2 '18 at 22:10
add a comment |
$begingroup$
Given the vectors
v1 = (a,b,c)
v2 = (d,e,f)
v3 = (x,y,z)
Where v1 and v3 are dependent ( I don't know yet ) and I am asked to calculate the span of the vectors, how would I do it?
If I calculate the determinat it will result 0 so it would only prove that it won't span the R^3, but what do I do next to prove if it spans ( or not ) R^2
linear-algebra vector-spaces
asked Dec 2 '18 at 22:05
Calin ChalyCalin Chaly
1
$endgroup$
Given the vectors
v1 = (a,b,c)
v2 = (d,e,f)
v3 = (x,y,z)
Where v1 and v3 are dependent ( I don't know yet ) and I am asked to calculate the span of the vectors, how would I do it?
If I calculate the determinat it will result 0 so it would only prove that it won't span the R^3, but what do I do next to prove if it spans ( or not ) R^2
linear-algebra vector-spaces
linear-algebra vector-spaces
asked Dec 2 '18 at 22:05
Calin ChalyCalin Chaly
1
asked Dec 2 '18 at 22:05
Calin ChalyCalin Chaly
1
asked Dec 2 '18 at 22:05
Calin ChalyCalin Chaly
1
asked Dec 2 '18 at 22:05
Calin ChalyCalin Chaly
1
asked Dec 2 '18 at 22:05
Calin ChalyCalin Chaly
1
1
$begingroup$
If $v_1$ and $v_3$ are dependant of each other, if one of them is non-zero, $v_1$ say, we know that $v_1 = kcdot v_3$, so span of this $3$ vectors would be span of $v_1$ and $v_2$.
$endgroup$
– Jakobian
Dec 2 '18 at 22:10
add a comment |
$begingroup$
If $v_1$ and $v_3$ are dependant of each other, if one of them is non-zero, $v_1$ say, we know that $v_1 = kcdot v_3$, so span of this $3$ vectors would be span of $v_1$ and $v_2$.
$endgroup$
– Jakobian
Dec 2 '18 at 22:10
$begingroup$
If $v_1$ and $v_3$ are dependant of each other, if one of them is non-zero, $v_1$ say, we know that $v_1 = kcdot v_3$, so span of this $3$ vectors would be span of $v_1$ and $v_2$.
$endgroup$
– Jakobian
Dec 2 '18 at 22:10
$begingroup$
If $v_1$ and $v_3$ are dependant of each other, if one of them is non-zero, $v_1$ say, we know that $v_1 = kcdot v_3$, so span of this $3$ vectors would be span of $v_1$ and $v_2$.
$endgroup$
– Jakobian
Dec 2 '18 at 22:10
add a comment |
0
active
oldest
votes
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%2f3023278%2fspanning-with-independent-and-dependent-vectors%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
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%2f3023278%2fspanning-with-independent-and-dependent-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
$begingroup$
If $v_1$ and $v_3$ are dependant of each other, if one of them is non-zero, $v_1$ say, we know that $v_1 = kcdot v_3$, so span of this $3$ vectors would be span of $v_1$ and $v_2$.
$endgroup$
– Jakobian
Dec 2 '18 at 22:10