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MATH2107-4-21

# MATH2107-4-21 - Section 4.2 Null Spaces Column Spaces and...

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Section 4.2 Null Spaces, Column Spaces and Linear Transformations Linear Algebra and its Applications David C. Lay — Winter 2008 – p. 1/16

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The technical/mechanics of this section are familar to us. The terminology is new. Let’s begin! The nullspace of a matrix is a subspace of the set of vectors on which the matrix acts. Let A be an n × n matrix and x R n . Multiplying A and x together we have A x R m . We can say when we perform the product A x that A acts on x ” or “ A transforms x — Winter 2008 – p. 2/16
From the latter statement we can think of the matrix A as representing a transformation which takes vectors from R n and transforms them into vectors in R m . We can denote this by T A : R n -→ R m x A x R m R n is called the domain of T A and the range of T A is the set of all images of R n under the transformation T A . The range of T A is denoted by rangeT A . R n and rangeT A are a vector space and subspace, respectively.

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MATH2107-4-21 - Section 4.2 Null Spaces Column Spaces and...

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