Question in Linear Algebra (Dimension of Vector Space)
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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
170k23132238
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
170k23132238
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
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@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
170k23132238
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
170k23132238
asked Jan 14 at 17:28
Maths UpPatMaths UpPat
112
edited Jan 14 at 17:30
José Carlos Santos
170k23132238
asked Jan 14 at 17:28
Maths UpPatMaths UpPat
112
edited Jan 14 at 17:30
José Carlos Santos
170k23132238
edited Jan 14 at 17:30
José Carlos Santos
170k23132238
edited Jan 14 at 17:30
José Carlos Santos
170k23132238
170k23132238
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 |
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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