- #1
xsqueetzzz
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Find a basis for the subspace of R^4 spanned by, S={(6,-3,6,340, (3,-2,3,19), (8,3,-9,6), (-2,0,6,-5)
Not too sure where to start.
Not too sure where to start.
A subspace is a subset of a vector space that satisfies all the properties of a vector space. This means that it is closed under vector addition and scalar multiplication, and contains the zero vector.
The dimension of a subspace is the number of vectors in a basis for that subspace. It is also equal to the number of linearly independent vectors in the subspace.
A subspace spans a vector space if every vector in that vector space can be written as a linear combination of the vectors in the subspace. In other words, the subspace contains enough vectors to reach every point in the vector space.
To find a basis for a subspace, you can use the process of elimination. Start with a set of vectors in the subspace and check if they are linearly independent. If not, remove one and check again until you have a set of linearly independent vectors. This set of vectors will be the basis for the subspace.
Yes, a subspace can have multiple bases. This is because there are often many different sets of vectors that can span a subspace. However, all bases for a subspace will have the same number of vectors, which is equal to the dimension of the subspace.