find the dimension of the given space?
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0
down vote
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let $W_1$ be the real vector space of all $5 times 2$ matrices of such that the sum the sum of the entries in each row is $0 $. let $W_2$be the real vector space of all $5 times 2$ matrices such that the sum of the entries in each column is zero .find the dimension of the space $W _1 cap W_2$
my attempts :$max[0,dim(W_1)+dim(W_2)- 5] le dim(W_1 ∩ W_2) le min[ dim(W_1) ,dim (W_2),]$
so $dim(W_1 ∩ W_2) = 2$
Am i right ?
linear-algebra
asked May 8 at 5:30
jasmine
1,331416
add a comment |
up vote
0
down vote
favorite
let $W_1$ be the real vector space of all $5 times 2$ matrices of such that the sum the sum of the entries in each row is $0 $. let $W_2$be the real vector space of all $5 times 2$ matrices such that the sum of the entries in each column is zero .find the dimension of the space $W _1 cap W_2$
my attempts :$max[0,dim(W_1)+dim(W_2)- 5] le dim(W_1 ∩ W_2) le min[ dim(W_1) ,dim (W_2),]$
so $dim(W_1 ∩ W_2) = 2$
Am i right ?
linear-algebra
asked May 8 at 5:30
jasmine
1,331416
1
You are not. I suppose that You calculate $dim(W_1)$ and $dim(W_2)$ in a wrong way. $dim(W_2)$ is much larger than $2$.
– Logic_Problem_42
May 8 at 5:34
1
I think the answer is 4. A row vector sums to 0 means it must have dimension 4. And since the columns sum to 0 once the first row is fixed the next row is negative of the first row.
– Piyush Divyanakar
May 8 at 5:38
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
let $W_1$ be the real vector space of all $5 times 2$ matrices of such that the sum the sum of the entries in each row is $0 $. let $W_2$be the real vector space of all $5 times 2$ matrices such that the sum of the entries in each column is zero .find the dimension of the space $W _1 cap W_2$
my attempts :$max[0,dim(W_1)+dim(W_2)- 5] le dim(W_1 ∩ W_2) le min[ dim(W_1) ,dim (W_2),]$
so $dim(W_1 ∩ W_2) = 2$
Am i right ?
linear-algebra
asked May 8 at 5:30
jasmine
1,331416
let $W_1$ be the real vector space of all $5 times 2$ matrices of such that the sum the sum of the entries in each row is $0 $. let $W_2$be the real vector space of all $5 times 2$ matrices such that the sum of the entries in each column is zero .find the dimension of the space $W _1 cap W_2$
my attempts :$max[0,dim(W_1)+dim(W_2)- 5] le dim(W_1 ∩ W_2) le min[ dim(W_1) ,dim (W_2),]$
so $dim(W_1 ∩ W_2) = 2$
Am i right ?
linear-algebra
linear-algebra
asked May 8 at 5:30
jasmine
1,331416
asked May 8 at 5:30
jasmine
1,331416
edited Nov 15 at 16:00
asked May 8 at 5:30
jasmine
1,331416
asked May 8 at 5:30
jasmine
1,331416
asked May 8 at 5:30
jasmine
1,331416
1,331416
1
You are not. I suppose that You calculate $dim(W_1)$ and $dim(W_2)$ in a wrong way. $dim(W_2)$ is much larger than $2$.
– Logic_Problem_42
May 8 at 5:34
1
I think the answer is 4. A row vector sums to 0 means it must have dimension 4. And since the columns sum to 0 once the first row is fixed the next row is negative of the first row.
– Piyush Divyanakar
May 8 at 5:38
add a comment |
1
You are not. I suppose that You calculate $dim(W_1)$ and $dim(W_2)$ in a wrong way. $dim(W_2)$ is much larger than $2$.
– Logic_Problem_42
May 8 at 5:34
1
I think the answer is 4. A row vector sums to 0 means it must have dimension 4. And since the columns sum to 0 once the first row is fixed the next row is negative of the first row.
– Piyush Divyanakar
May 8 at 5:38
1
1
You are not. I suppose that You calculate $dim(W_1)$ and $dim(W_2)$ in a wrong way. $dim(W_2)$ is much larger than $2$.
– Logic_Problem_42
May 8 at 5:34
You are not. I suppose that You calculate $dim(W_1)$ and $dim(W_2)$ in a wrong way. $dim(W_2)$ is much larger than $2$.
– Logic_Problem_42
May 8 at 5:34
1
1
I think the answer is 4. A row vector sums to 0 means it must have dimension 4. And since the columns sum to 0 once the first row is fixed the next row is negative of the first row.
– Piyush Divyanakar
May 8 at 5:38
I think the answer is 4. A row vector sums to 0 means it must have dimension 4. And since the columns sum to 0 once the first row is fixed the next row is negative of the first row.
– Piyush Divyanakar
May 8 at 5:38
add a comment |
1 Answer
1
active
oldest
votes
up vote
4
down vote
accepted
Elements of $W_1 cap W_2$ satisfy the condition that the sum of each row and each column is $0$.
Hence the first row completely determines the next row and the first $4$ entries of the first row would determine the $5$ element, hence the dimension is $4$.
answered May 8 at 6:23
Siong Thye Goh
94.3k1462114
thanks Siong THye
– jasmine
May 8 at 7:43
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
4
down vote
accepted
Elements of $W_1 cap W_2$ satisfy the condition that the sum of each row and each column is $0$.
Hence the first row completely determines the next row and the first $4$ entries of the first row would determine the $5$ element, hence the dimension is $4$.
answered May 8 at 6:23
Siong Thye Goh
94.3k1462114
thanks Siong THye
– jasmine
May 8 at 7:43
add a comment |
up vote
4
down vote
accepted
Elements of $W_1 cap W_2$ satisfy the condition that the sum of each row and each column is $0$.
Hence the first row completely determines the next row and the first $4$ entries of the first row would determine the $5$ element, hence the dimension is $4$.
answered May 8 at 6:23
Siong Thye Goh
94.3k1462114
thanks Siong THye
– jasmine
May 8 at 7:43
add a comment |
up vote
4
down vote
accepted
up vote
4
down vote
accepted
Elements of $W_1 cap W_2$ satisfy the condition that the sum of each row and each column is $0$.
Hence the first row completely determines the next row and the first $4$ entries of the first row would determine the $5$ element, hence the dimension is $4$.
answered May 8 at 6:23
Siong Thye Goh
94.3k1462114
Elements of $W_1 cap W_2$ satisfy the condition that the sum of each row and each column is $0$.
Hence the first row completely determines the next row and the first $4$ entries of the first row would determine the $5$ element, hence the dimension is $4$.
answered May 8 at 6:23
Siong Thye Goh
94.3k1462114
answered May 8 at 6:23
Siong Thye Goh
94.3k1462114
answered May 8 at 6:23
Siong Thye Goh
94.3k1462114
answered May 8 at 6:23
Siong Thye Goh
94.3k1462114
94.3k1462114
thanks Siong THye
– jasmine
May 8 at 7:43
add a comment |
thanks Siong THye
– jasmine
May 8 at 7:43
thanks Siong THye
– jasmine
May 8 at 7:43
thanks Siong THye
– jasmine
May 8 at 7:43
add a comment |
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You are not. I suppose that You calculate $dim(W_1)$ and $dim(W_2)$ in a wrong way. $dim(W_2)$ is much larger than $2$.
– Logic_Problem_42
May 8 at 5:34
1
I think the answer is 4. A row vector sums to 0 means it must have dimension 4. And since the columns sum to 0 once the first row is fixed the next row is negative of the first row.
– Piyush Divyanakar
May 8 at 5:38