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LosTacos
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Homework Statement
Let L: ℝn→ℝm be a linear transformation with matrix A ( with respect to the standard basis). Show that ker(L) is the orthogonal complement of the row space of A.
Homework Equations
The Attempt at a Solution
The ker(L) is the subset of all vectors of V that map to 0. The orthogonal complement of W is the set of all vectors x with property that xw= 0. Would we use the dimension theorem:
dim(ker(L)) = n - dim(range(L)) = n - dim(W) =dim(Wτ). Since Wτ is contained in ker(L).
*Wτ is orthogonal complement.