Mathematics, 21.08.2019 19:30 clarissa2006
L: v --> w is a linear transformation. prove each of the following (a) ker l is a subspace of v. (b) range l is a subspace of w.
Answers: 1
, and 
is a scalar (a real or complex number).
is not empty. This is easy because 
, by linearity. Here, 
stands for the zero vector of V, and 
stands for the zero vector of W.
. By linearity
.
. Again, by linearity
.
and 
are in range of 
. Then, there exist 
such that 
and 
.
is on the range of 
.
such that 
. Thus 
is in the range of 
.
. Thus 
is in the range of Another question on Mathematics
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L: v --> w is a linear transformation. prove each of the following (a) ker l is a subspace of v....
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