Elements of the smallest subspace containing certain vectors
$begingroup$
List the elements of the smallest subspace of $mathbb{Z}^{4}_{5}$ containing the following vectors: $(0,0,0,4)^T, (2,4,3,2)^T, (1,2,4,3)^T$:
Now from the definition I know that the subspace I'm looking for is the span of the following vectors, which should have 25 elements.
My question is, is there a systematic approach for finding all of these elements or do I have to brute force it by multiplying each of these vectors by some $a in mathbb{Z}_{5}$, adding them together and so on, just to find every element of the span?
linear-algebra vector-spaces
asked Jan 15 at 20:27
J. LastinJ. Lastin
14810
$endgroup$
add a comment |
$begingroup$
List the elements of the smallest subspace of $mathbb{Z}^{4}_{5}$ containing the following vectors: $(0,0,0,4)^T, (2,4,3,2)^T, (1,2,4,3)^T$:
Now from the definition I know that the subspace I'm looking for is the span of the following vectors, which should have 25 elements.
My question is, is there a systematic approach for finding all of these elements or do I have to brute force it by multiplying each of these vectors by some $a in mathbb{Z}_{5}$, adding them together and so on, just to find every element of the span?
linear-algebra vector-spaces
asked Jan 15 at 20:27
J. LastinJ. Lastin
14810
$endgroup$
add a comment |
$begingroup$
List the elements of the smallest subspace of $mathbb{Z}^{4}_{5}$ containing the following vectors: $(0,0,0,4)^T, (2,4,3,2)^T, (1,2,4,3)^T$:
Now from the definition I know that the subspace I'm looking for is the span of the following vectors, which should have 25 elements.
My question is, is there a systematic approach for finding all of these elements or do I have to brute force it by multiplying each of these vectors by some $a in mathbb{Z}_{5}$, adding them together and so on, just to find every element of the span?
linear-algebra vector-spaces
asked Jan 15 at 20:27
J. LastinJ. Lastin
14810
$endgroup$
List the elements of the smallest subspace of $mathbb{Z}^{4}_{5}$ containing the following vectors: $(0,0,0,4)^T, (2,4,3,2)^T, (1,2,4,3)^T$:
Now from the definition I know that the subspace I'm looking for is the span of the following vectors, which should have 25 elements.
My question is, is there a systematic approach for finding all of these elements or do I have to brute force it by multiplying each of these vectors by some $a in mathbb{Z}_{5}$, adding them together and so on, just to find every element of the span?
linear-algebra vector-spaces
linear-algebra vector-spaces
asked Jan 15 at 20:27
J. LastinJ. Lastin
14810
asked Jan 15 at 20:27
J. LastinJ. Lastin
14810
asked Jan 15 at 20:27
J. LastinJ. Lastin
14810
asked Jan 15 at 20:27
J. LastinJ. Lastin
14810
asked Jan 15 at 20:27
J. LastinJ. Lastin
14810
14810
add a comment |
add a comment |
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