Solution:
Note: Given transformation is not valid
it should be defined as
is defined by
a). Let
we have
Hence, is a linear transformation.
Now, Let the standard basis for and are respectively
and
Now,
Thus, matrix representation is
Which is the required matrix representation.
b).
Now, Kernel of is given by
applying
applying
applying
Thus, the basis for is
c). we have
applying
applying
applying
applying
Thus, the basis for is given by
which is the required basis.
This complete the solution.
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