4.7 - MATH1850U/2050U Chapter 4 cont GENERAL VECTOR SPACES...

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MATH1850U/2050U: Chapter 4 cont. .. 1 GENERAL VECTOR SPACES cont. .. Row Space, Column Space, and Null Space (4.7; pg. 225) Definition: For an n m matrix mn m m n n a a a a a a a a a A 2 1 2 22 21 1 12 11 , the vectors in R n formed from the rows of A are called the row vectors of A , and the vectors in R m formed from the columns of A are called the column vectors of A . Example: Identify the row vectors and column vectors of the matrix below. Definition: If A is an n m matrix, then the subspace of R n spanned by the row vectors of A is called the row space of A , and the subspace of R m spanned by the column vectors of A is called the column space of A . The solution space of the homogeneous system of equations 0 x A , which is a subspace of R n , is called the nullspace of A . Theorem: A system of linear equations b x A is consistent if and only if b is in the column space of A .
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4.7 - MATH1850U/2050U Chapter 4 cont GENERAL VECTOR SPACES...

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