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Answer:
The image of through T is
Step-by-step explanation:
We know that
→
is a linear transformation that maps
into
⇒
And also maps into
⇒
We need to find the image of the vector
We know that exists a matrix A from (because of how T was defined) such that :
for all x ∈
We can find the matrix A by applying T to a base of the domain ().
Notice that we have that data :
{
}
Being the cannonic base of
The following step is to put the images from the vectors of the base into the columns of the new matrix A :
(Data of the problem)
(Data of the problem)
Writing the matrix A :
Now with the matrix A we can find the image of such as :
⇒
We found out that the image of through T is the vector