Question

Let e1, . . . , en be the n elementary vectors in Rn. Consider the...

Let e1, . . . , en be the n elementary vectors in Rn. Consider the linear transfor- mation T : Rn → Rn satisfying the following equations:

T(e1) = e1−e2

T(e2) = e2−e3

. .
T(en) = en−e1.

(a) What is ker(T)?

(b) What is im(T)?

(c) Let In : Rn → Rn be the identity linear transformation. Is the linear transformation T − In invertible? Justify your answer. (If it is invertible, you do not need to solve for the inverse.)

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ask if you have any questions. Tgank you

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