- #1
dracolnyte
- 28
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Homework Statement
(i)Show that the linear span of the vector a1 = (-7, 8, 5) is the line whose equation is
x/(-7) = y/8 = z/5
The Attempt at a Solution
The problem is, I don't know where or how to start.
A subspace is a subset of a vector space that satisfies the properties of a vector space. This means that it is closed under addition and scalar multiplication, and contains the zero vector.
A subspace is a subset of a vector space, while a span is the set of all possible linear combinations of a given set of vectors. A subspace is a subset of a span, but a span may not necessarily be a subspace.
A set of vectors spans a subspace if every vector in the subspace can be written as a linear combination of the given vectors. This can be checked by setting up a system of equations and solving for the coefficients of the linear combination.
The dimension of a subspace is the number of linearly independent vectors needed to span the subspace. It is also equal to the number of elements in a basis for the subspace.
No, a subspace can only have a finite number of dimensions. This is because a subspace is a subset of a vector space, which is a finite dimensional object.