← MATH 01210 · Linear Algebra
MATH 01210 · Vector spaces
Null/column space, rank-nullity
Definition
Null space N(A)={x|Ax=0}. Column space C(A)=span of columns. Rank = dim C(A) = number of pivots. Rank-nullity: rank(A)+nullity(A)=n for A m×n.
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Nullity = dim N(A) = number of free variables.
Ax=b solvable iff b ∈ C(A).
Row space has same dimension as column space (the rank).
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1.For a 3×5 matrix of rank 2, find nullity.