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linear alg please answer all of 4, if you dont want to answer 2 4. Let...

4. Let T: R4 + R3 be the transformation T(7) = A7 where A is the following matrix: . 1 1 0 1 A=-2 4 2 2 -1 8 3 5 (a) Find a b

2. Let T(T) = Af and S(T) = Bī be the transformations that correspond to the following matrices: A= C. 3 -1 0 1 2 2 1 3 2 1 -

(b) Find the image T(T) of ī= 3 2 (e) Find the image S(y) where y is your answer to (b). (d) The composition SoT is the trans

linear alg please answer all of 4, if you dont want to answer 2

4. Let T: R4 + R3 be the transformation T(7) = A7 where A is the following matrix: . 1 1 0 1 A=-2 4 2 2 -1 8 3 5 (a) Find a basis for the range of T and its dimension. (b) The preimage of 7 is the set of all 7 € R4 such that T(T) = 7. Explain how the preimage of o is related to the null space of A. (c) Find a basis for the preimage of 7 and its dimension.
2. Let T(T) = Af and S(T) = Bī be the transformations that correspond to the following matrices: A= C. 3 -1 0 1 2 2 1 3 2 1 -1 0 2 1 2
(b) Find the image T(T) of ī= 3 2 (e) Find the image S(y) where y is your answer to (b). (d) The composition SoT is the transformation defined by SoT(T) = S(T(7)). Find the image SoT(T) of t= ( 3 2
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