Question in Linear Algebra (Dimension of Vector Space)
$begingroup$
I have stucked in an exercise in Linear Algebra.
We have a vector space V and the subspaces $V_{1},V_{2}$ of $V$.
If we know that $dim V=12$, $dim V_{1}=8$ and $dim V_{2}=10$,then
we want to calculate the $dim V_{1}cap V_{2}$.
I have found from identity $dim V=12gedim(V_{1}+V_{2})=dim V_{1}+dim V_{2}-dim V_{1}cap V_{2}$ and from inequality $dim V_{1}cap V_{2}le dim V_{1}=8$,that $dim V_{1}cap V_{2}in {6,7,8}$
linear-algebra vector-spaces
edited Jan 14 at 17:30
José Carlos Santos
176k24137246
asked Jan 14 at 17:28
Maths UpPatMaths UpPat
112
$endgroup$
add a comment |
$begingroup$
I have stucked in an exercise in Linear Algebra.
We have a vector space V and the subspaces $V_{1},V_{2}$ of $V$.
If we know that $dim V=12$, $dim V_{1}=8$ and $dim V_{2}=10$,then
we want to calculate the $dim V_{1}cap V_{2}$.
I have found from identity $dim V=12gedim(V_{1}+V_{2})=dim V_{1}+dim V_{2}-dim V_{1}cap V_{2}$ and from inequality $dim V_{1}cap V_{2}le dim V_{1}=8$,that $dim V_{1}cap V_{2}in {6,7,8}$
linear-algebra vector-spaces
edited Jan 14 at 17:30
José Carlos Santos
176k24137246
asked Jan 14 at 17:28
Maths UpPatMaths UpPat
112
$endgroup$
1
$begingroup$
Welcome to MSE. Is there a question here?
$endgroup$
– José Carlos Santos
Jan 14 at 17:29
3
$begingroup$
Without more information you cannot get a better answer than what you have.
$endgroup$
– SvanN
Jan 14 at 17:29
$begingroup$
@JoséCarlosSantos “Then we want to calculate...”
$endgroup$
– SvanN
Jan 14 at 17:29
$begingroup$
Is $V$ possibly the union of $V_1$ and $V_2$?
$endgroup$
– lightxbulb
Jan 14 at 17:42
$begingroup$
we dont have more information for V
$endgroup$
– Maths UpPat
Jan 14 at 17:46
add a comment |
$begingroup$
I have stucked in an exercise in Linear Algebra.
We have a vector space V and the subspaces $V_{1},V_{2}$ of $V$.
If we know that $dim V=12$, $dim V_{1}=8$ and $dim V_{2}=10$,then
we want to calculate the $dim V_{1}cap V_{2}$.
I have found from identity $dim V=12gedim(V_{1}+V_{2})=dim V_{1}+dim V_{2}-dim V_{1}cap V_{2}$ and from inequality $dim V_{1}cap V_{2}le dim V_{1}=8$,that $dim V_{1}cap V_{2}in {6,7,8}$
linear-algebra vector-spaces
edited Jan 14 at 17:30
José Carlos Santos
176k24137246
asked Jan 14 at 17:28
Maths UpPatMaths UpPat
112
$endgroup$
I have stucked in an exercise in Linear Algebra.
We have a vector space V and the subspaces $V_{1},V_{2}$ of $V$.
If we know that $dim V=12$, $dim V_{1}=8$ and $dim V_{2}=10$,then
we want to calculate the $dim V_{1}cap V_{2}$.
I have found from identity $dim V=12gedim(V_{1}+V_{2})=dim V_{1}+dim V_{2}-dim V_{1}cap V_{2}$ and from inequality $dim V_{1}cap V_{2}le dim V_{1}=8$,that $dim V_{1}cap V_{2}in {6,7,8}$
linear-algebra vector-spaces
linear-algebra vector-spaces
edited Jan 14 at 17:30
José Carlos Santos
176k24137246
asked Jan 14 at 17:28
Maths UpPatMaths UpPat
112
edited Jan 14 at 17:30
José Carlos Santos
176k24137246
asked Jan 14 at 17:28
Maths UpPatMaths UpPat
112
edited Jan 14 at 17:30
José Carlos Santos
176k24137246
edited Jan 14 at 17:30
José Carlos Santos
176k24137246
edited Jan 14 at 17:30
José Carlos Santos
176k24137246
176k24137246
asked Jan 14 at 17:28
Maths UpPatMaths UpPat
112
asked Jan 14 at 17:28
Maths UpPatMaths UpPat
112
asked Jan 14 at 17:28
Maths UpPatMaths UpPat
112
112
1
$begingroup$
Welcome to MSE. Is there a question here?
$endgroup$
– José Carlos Santos
Jan 14 at 17:29
3
$begingroup$
Without more information you cannot get a better answer than what you have.
$endgroup$
– SvanN
Jan 14 at 17:29
$begingroup$
@JoséCarlosSantos “Then we want to calculate...”
$endgroup$
– SvanN
Jan 14 at 17:29
$begingroup$
Is $V$ possibly the union of $V_1$ and $V_2$?
$endgroup$
– lightxbulb
Jan 14 at 17:42
$begingroup$
we dont have more information for V
$endgroup$
– Maths UpPat
Jan 14 at 17:46
add a comment |
1
$begingroup$
Welcome to MSE. Is there a question here?
$endgroup$
– José Carlos Santos
Jan 14 at 17:29
3
$begingroup$
Without more information you cannot get a better answer than what you have.
$endgroup$
– SvanN
Jan 14 at 17:29
$begingroup$
@JoséCarlosSantos “Then we want to calculate...”
$endgroup$
– SvanN
Jan 14 at 17:29
$begingroup$
Is $V$ possibly the union of $V_1$ and $V_2$?
$endgroup$
– lightxbulb
Jan 14 at 17:42
$begingroup$
we dont have more information for V
$endgroup$
– Maths UpPat
Jan 14 at 17:46
1
1
$begingroup$
Welcome to MSE. Is there a question here?
$endgroup$
– José Carlos Santos
Jan 14 at 17:29
$begingroup$
Welcome to MSE. Is there a question here?
$endgroup$
– José Carlos Santos
Jan 14 at 17:29
3
3
$begingroup$
Without more information you cannot get a better answer than what you have.
$endgroup$
– SvanN
Jan 14 at 17:29
$begingroup$
Without more information you cannot get a better answer than what you have.
$endgroup$
– SvanN
Jan 14 at 17:29
$begingroup$
@JoséCarlosSantos “Then we want to calculate...”
$endgroup$
– SvanN
Jan 14 at 17:29
$begingroup$
@JoséCarlosSantos “Then we want to calculate...”
$endgroup$
– SvanN
Jan 14 at 17:29
$begingroup$
Is $V$ possibly the union of $V_1$ and $V_2$?
$endgroup$
– lightxbulb
Jan 14 at 17:42
$begingroup$
Is $V$ possibly the union of $V_1$ and $V_2$?
$endgroup$
– lightxbulb
Jan 14 at 17:42
$begingroup$
we dont have more information for V
$endgroup$
– Maths UpPat
Jan 14 at 17:46
$begingroup$
we dont have more information for V
$endgroup$
– Maths UpPat
Jan 14 at 17:46
add a comment |
0
active
oldest
votes
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
});
}
});
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%2f3073491%2fquestion-in-linear-algebra-dimension-of-vector-space%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%2f3073491%2fquestion-in-linear-algebra-dimension-of-vector-space%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
1
$begingroup$
Welcome to MSE. Is there a question here?
$endgroup$
– José Carlos Santos
Jan 14 at 17:29
3
$begingroup$
Without more information you cannot get a better answer than what you have.
$endgroup$
– SvanN
Jan 14 at 17:29
$begingroup$
@JoséCarlosSantos “Then we want to calculate...”
$endgroup$
– SvanN
Jan 14 at 17:29
$begingroup$
Is $V$ possibly the union of $V_1$ and $V_2$?
$endgroup$
– lightxbulb
Jan 14 at 17:42
$begingroup$
we dont have more information for V
$endgroup$
– Maths UpPat
Jan 14 at 17:46