Kernels and Images of Matrix

Monday, 27 August 2018

9:16 AM

Of a matrix

 

 

Infinitely many solutions, so set the non-leading variables as parameters

,
Row 2: .  

 

 

 is the solution set of  where

 

 

 

 is the set of all vectors of the form

 

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If  is a linear map, then

1.  is a subspace of the domain

We call  the nullity of T, denoted by

2.  is a supspace of the codomain

We call  the rank of T, denoted by

 

If  is an  matrix then

1.  is a suspace of

We call  the nullity of A, denoted by

2.  is a suspace of

We call  the rank of A, denoted by

 

So a basis for

 

A basis for