Mixing
linear algebra - spaces and subspaces
$begingroup$
Let $U ne {0}$ be a sub-space of a finite-dimensional vector space $V$. Assume that there exists a unique subspace $W subset V$, such that $V = U oplus W$. Prove that $U = V$.
I don't know how to start. please give me some guidelines...
linear-algebra vector-spaces
edited Jan 28 at 16:12
gt6989b
35.2k22557
asked Jan 28 at 16:07
user3523226user3523226
357
$endgroup$
add a comment |
$begingroup$
Let $U ne {0}$ be a sub-space of a finite-dimensional vector space $V$. Assume that there exists a unique subspace $W subset V$, such that $V = U oplus W$. Prove that $U = V$.
I don't know how to start. please give me some guidelines...
linear-algebra vector-spaces
edited Jan 28 at 16:12
gt6989b
35.2k22557
asked Jan 28 at 16:07
user3523226user3523226
357
$endgroup$
1
$begingroup$
Please do not ask questions that consist only of a problem statement and "I don't know how to start." These don't make good questions and they aren't a good fit for this site. See the advice here.
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– Trevor Gunn
Jan 28 at 16:14
add a comment |
$begingroup$
Let $U ne {0}$ be a sub-space of a finite-dimensional vector space $V$. Assume that there exists a unique subspace $W subset V$, such that $V = U oplus W$. Prove that $U = V$.
I don't know how to start. please give me some guidelines...
linear-algebra vector-spaces
edited Jan 28 at 16:12
gt6989b
35.2k22557
asked Jan 28 at 16:07
user3523226user3523226
357
$endgroup$
Let $U ne {0}$ be a sub-space of a finite-dimensional vector space $V$. Assume that there exists a unique subspace $W subset V$, such that $V = U oplus W$. Prove that $U = V$.
I don't know how to start. please give me some guidelines...
linear-algebra vector-spaces
linear-algebra vector-spaces
edited Jan 28 at 16:12
gt6989b
35.2k22557
asked Jan 28 at 16:07
user3523226user3523226
357
edited Jan 28 at 16:12
gt6989b
35.2k22557
asked Jan 28 at 16:07
user3523226user3523226
357
edited Jan 28 at 16:12
gt6989b
35.2k22557
edited Jan 28 at 16:12
gt6989b
35.2k22557
edited Jan 28 at 16:12
gt6989b
35.2k22557
35.2k22557
asked Jan 28 at 16:07
user3523226user3523226
357
asked Jan 28 at 16:07
user3523226user3523226
357
asked Jan 28 at 16:07
user3523226user3523226
357
357
1
$begingroup$
Please do not ask questions that consist only of a problem statement and "I don't know how to start." These don't make good questions and they aren't a good fit for this site. See the advice here.
$endgroup$
– Trevor Gunn
Jan 28 at 16:14
add a comment |
1
$begingroup$
Please do not ask questions that consist only of a problem statement and "I don't know how to start." These don't make good questions and they aren't a good fit for this site. See the advice here.
$endgroup$
– Trevor Gunn
Jan 28 at 16:14
1
1
$begingroup$
Please do not ask questions that consist only of a problem statement and "I don't know how to start." These don't make good questions and they aren't a good fit for this site. See the advice here.
$endgroup$
– Trevor Gunn
Jan 28 at 16:14
$begingroup$
Please do not ask questions that consist only of a problem statement and "I don't know how to start." These don't make good questions and they aren't a good fit for this site. See the advice here.
$endgroup$
– Trevor Gunn
Jan 28 at 16:14
add a comment |
1 Answer
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HINT
Prove that $W$ is also a subspace of $V$, then by uniqueness of $U$, it must be that $W = U$ or $W = {0}$.
answered Jan 28 at 16:15
gt6989bgt6989b
35.2k22557
$endgroup$
add a comment |
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$begingroup$
HINT
Prove that $W$ is also a subspace of $V$, then by uniqueness of $U$, it must be that $W = U$ or $W = {0}$.
answered Jan 28 at 16:15
gt6989bgt6989b
35.2k22557
$endgroup$
add a comment |
$begingroup$
HINT
Prove that $W$ is also a subspace of $V$, then by uniqueness of $U$, it must be that $W = U$ or $W = {0}$.
answered Jan 28 at 16:15
gt6989bgt6989b
35.2k22557
$endgroup$
add a comment |
$begingroup$
HINT
Prove that $W$ is also a subspace of $V$, then by uniqueness of $U$, it must be that $W = U$ or $W = {0}$.
answered Jan 28 at 16:15
gt6989bgt6989b
35.2k22557
$endgroup$
HINT
Prove that $W$ is also a subspace of $V$, then by uniqueness of $U$, it must be that $W = U$ or $W = {0}$.
answered Jan 28 at 16:15
gt6989bgt6989b
35.2k22557
answered Jan 28 at 16:15
gt6989bgt6989b
35.2k22557
answered Jan 28 at 16:15
gt6989bgt6989b
35.2k22557
answered Jan 28 at 16:15
gt6989bgt6989b
35.2k22557
35.2k22557
add a comment |
add a comment |
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$begingroup$
Please do not ask questions that consist only of a problem statement and "I don't know how to start." These don't make good questions and they aren't a good fit for this site. See the advice here.
$endgroup$
– Trevor Gunn
Jan 28 at 16:14