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Unformatted text preview: MATH1850U/2050U: Chapter 4 cont... 1 GENERAL VECTOR SPACES cont... Rank, Nullity, and the Fundamental Matrix Spaces (4.8; pg. 237) Note: If we have matrix A and its transpose A T , there are 4 vectors spaces of interest 1) row space of A 2) column space of A 3) nullspace of A 4) nullspace of A T Remarks: Here are a few interesting properties for the spaces associated with an n m matrix A : the row space of A T is the column space of A and vice versa the row space and null space of A are subspaces of R n the column space of A and null space of A T are subspaces of R m Definition: The common dimension of the row and column space of a matrix A is called the rank of A and is denoted by rank( A ). The dimension of the nullspace of A is called the nullity of A and is denoted by nullity( A ). Application: The concept of rank is used to help find efficient methods for transmitting large amounts of digital data (see pg. 245 for more details)....
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