when two sets of vectors have the same all linear combinations?
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I don't know how to solve this kind of question this is my issue firstly I'm given tow sets of vectors S,T
S={v1,v2,v3,v4} this one is dependent
T={v1,v2,v4} this one is independent
as you may notice the set T is a subset of S which has the same vectors except {v3} then how to show that the two sets have the same all linear combinations?
linear-algebra
asked Nov 19 at 9:42
faisal
122
add a comment |
up vote
0
down vote
favorite
I don't know how to solve this kind of question this is my issue firstly I'm given tow sets of vectors S,T
S={v1,v2,v3,v4} this one is dependent
T={v1,v2,v4} this one is independent
as you may notice the set T is a subset of S which has the same vectors except {v3} then how to show that the two sets have the same all linear combinations?
linear-algebra
asked Nov 19 at 9:42
faisal
122
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I don't know how to solve this kind of question this is my issue firstly I'm given tow sets of vectors S,T
S={v1,v2,v3,v4} this one is dependent
T={v1,v2,v4} this one is independent
as you may notice the set T is a subset of S which has the same vectors except {v3} then how to show that the two sets have the same all linear combinations?
linear-algebra
asked Nov 19 at 9:42
faisal
122
I don't know how to solve this kind of question this is my issue firstly I'm given tow sets of vectors S,T
S={v1,v2,v3,v4} this one is dependent
T={v1,v2,v4} this one is independent
as you may notice the set T is a subset of S which has the same vectors except {v3} then how to show that the two sets have the same all linear combinations?
linear-algebra
linear-algebra
asked Nov 19 at 9:42
faisal
122
asked Nov 19 at 9:42
faisal
122
asked Nov 19 at 9:42
faisal
122
asked Nov 19 at 9:42
faisal
122
asked Nov 19 at 9:42
faisal
122
122
add a comment |
add a comment |
1 Answer
1
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1
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accepted
We just have to show that $v_3$ can be expressed as a linear combination of $v_1, v_2, v_4$.
Hence adding $v_3$ doesn't change the span.
answered Nov 19 at 9:46
Siong Thye Goh
97k1462116
sorry, sir could you please explain what does it mean when two sets of vectors have the same all linear combinations?
– faisal
Nov 19 at 11:03
If we let $A = span{ v_1, v_2, v_3, v_4}$ and $B = span{ v_1, v_2, v_4}$. Then the two sets $A$ and $B$ are the same.
– Siong Thye Goh
Nov 19 at 11:46
thank you, sir, you are really great
– faisal
Nov 19 at 11:56
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
We just have to show that $v_3$ can be expressed as a linear combination of $v_1, v_2, v_4$.
Hence adding $v_3$ doesn't change the span.
answered Nov 19 at 9:46
Siong Thye Goh
97k1462116
sorry, sir could you please explain what does it mean when two sets of vectors have the same all linear combinations?
– faisal
Nov 19 at 11:03
If we let $A = span{ v_1, v_2, v_3, v_4}$ and $B = span{ v_1, v_2, v_4}$. Then the two sets $A$ and $B$ are the same.
– Siong Thye Goh
Nov 19 at 11:46
thank you, sir, you are really great
– faisal
Nov 19 at 11:56
add a comment |
up vote
1
down vote
accepted
We just have to show that $v_3$ can be expressed as a linear combination of $v_1, v_2, v_4$.
Hence adding $v_3$ doesn't change the span.
answered Nov 19 at 9:46
Siong Thye Goh
97k1462116
sorry, sir could you please explain what does it mean when two sets of vectors have the same all linear combinations?
– faisal
Nov 19 at 11:03
If we let $A = span{ v_1, v_2, v_3, v_4}$ and $B = span{ v_1, v_2, v_4}$. Then the two sets $A$ and $B$ are the same.
– Siong Thye Goh
Nov 19 at 11:46
thank you, sir, you are really great
– faisal
Nov 19 at 11:56
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
We just have to show that $v_3$ can be expressed as a linear combination of $v_1, v_2, v_4$.
Hence adding $v_3$ doesn't change the span.
answered Nov 19 at 9:46
Siong Thye Goh
97k1462116
We just have to show that $v_3$ can be expressed as a linear combination of $v_1, v_2, v_4$.
Hence adding $v_3$ doesn't change the span.
answered Nov 19 at 9:46
Siong Thye Goh
97k1462116
answered Nov 19 at 9:46
Siong Thye Goh
97k1462116
answered Nov 19 at 9:46
Siong Thye Goh
97k1462116
answered Nov 19 at 9:46
Siong Thye Goh
97k1462116
97k1462116
sorry, sir could you please explain what does it mean when two sets of vectors have the same all linear combinations?
– faisal
Nov 19 at 11:03
If we let $A = span{ v_1, v_2, v_3, v_4}$ and $B = span{ v_1, v_2, v_4}$. Then the two sets $A$ and $B$ are the same.
– Siong Thye Goh
Nov 19 at 11:46
thank you, sir, you are really great
– faisal
Nov 19 at 11:56
add a comment |
sorry, sir could you please explain what does it mean when two sets of vectors have the same all linear combinations?
– faisal
Nov 19 at 11:03
If we let $A = span{ v_1, v_2, v_3, v_4}$ and $B = span{ v_1, v_2, v_4}$. Then the two sets $A$ and $B$ are the same.
– Siong Thye Goh
Nov 19 at 11:46
thank you, sir, you are really great
– faisal
Nov 19 at 11:56
sorry, sir could you please explain what does it mean when two sets of vectors have the same all linear combinations?
– faisal
Nov 19 at 11:03
sorry, sir could you please explain what does it mean when two sets of vectors have the same all linear combinations?
– faisal
Nov 19 at 11:03
If we let $A = span{ v_1, v_2, v_3, v_4}$ and $B = span{ v_1, v_2, v_4}$. Then the two sets $A$ and $B$ are the same.
– Siong Thye Goh
Nov 19 at 11:46
If we let $A = span{ v_1, v_2, v_3, v_4}$ and $B = span{ v_1, v_2, v_4}$. Then the two sets $A$ and $B$ are the same.
– Siong Thye Goh
Nov 19 at 11:46
thank you, sir, you are really great
– faisal
Nov 19 at 11:56
thank you, sir, you are really great
– faisal
Nov 19 at 11:56
add a comment |
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