Unformatted text preview: by using the following steps: (a) Denote H = null( T ◦ S ) (a linear subspace of U ), and deﬁne a linear transformation R : H → V by R ( v ) = S ( v ) (i.e., it is the same as S , but its domain is a subspace of the domain of S ; sometimes R deﬁned in this way will be referred to as the restriction of S to H ). Show that null( S ) ⊆ H , and explain why this implies that null( R ) = null( S ). (b) Show that range( R ) ⊆ null( T ). (c) Apply the dimension formula (Theorem 6.5.1 in the textbook) for a suitable linear transformation to deduce the inequality stated at the beginning of the question....
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 Fall '07
 Schilling
 Math, Linear Algebra, Algebra, Vector Space, linear transformation, Solve calculational exercises

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