Question

18. Let T be the matrix transformation T -1 2 0 -1 2 2 -1 h 2 -3 k 4 a. What are the domain and codomain of T? b. Find the REF of [T]. Hint: You'll need the REF in some of the following questions. -1 -1 -1 -3 (REF of [7]= 0 2 2 4 is given here so that you can correctly answer the following 0 0 h – 2 k-6 questions.) c. Define the range of T. How is it related to the standard matrix [T]? d. Does the vector 1 belong to the range of T when h = 2 and k = 6 ? Justify your answer! 1 e. Find a basis and the dimension for the range of T İ. when h = 2 and k = 6 ? What geometric object in R3 is the range of T? Justify your answer! ii. when h = 2 and k = 6? What is the range of T? Justify your answer! f. For what values of k is T onto when h = 2 ? Justify your answer! g. Is T one-to-one? Justify your answer! h. Define the kernel of T. i. Find the kernel of T when h = 2 and k = 6. and find a basis and the dimension for the kernel of T. ii. Find the kernel of T when h = 2 and .k = 7 and find a basis and the dimension for the kernel of T.

Answer 1

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