Vector Spaces - Null Spaces, Column Spaces, and Linear Transformations
4 important questions on Vector Spaces - Null Spaces, Column Spaces, and Linear Transformations
The null space of an m x n matrix A, written as Nul(A), is?
Nul A = {x : x is in Rn and Ax = 0}
Theorem 2
The null space of an m x n matrix A is a subspace of Rn. What set of solutions is also a subspace of Rn?
The column space of an m x n matrix A, written as Col A, is?
Col A = Span{a1, ..., an}
NOTE THE SPAN
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Theorem 3
The column space of an m x n matrix A is which subspace?
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