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6.6 Column space, row space, and rank
Use row reduction and basis ideas together to read column space, row space, and rank without confusing what row operations actually preserve.
Course contents
MATH1030: Linear algebra I
Linear algebra notes.
3.13.1 Matrix multiplication and identity matrices3.23.2 Transpose and special matrices3.33.3 Row-operation matrices3.13.1 Matrix addition, subtraction, and scalar multiplication3.23.2 Matrix multiplication and linear systems3.33.3 Transposes, symmetric matrices, and skew-symmetric matrices3.43.4 Special matrices3.53.5 Block matrices
6.16.1 Vector spacesMember6.26.2 SubspacesMember6.36.3 Linear combinations and spanMember6.46.4 Linear dependence and independenceMember6.56.5 Basis and dimensionMember6.66.6 Column space, row space, and rankCurrent sectionMember6.76.7 Matrix subspaces, basis, and dimensionMember6.86.8 Basis extension and change of basisMember
Prerequisites
Key terms in this unit
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