Vector Spaces and linear Transformations

[Raay]

Hello I have a maths midterm exam tomorrow and this question is from a tutorial I was absent on. Can any on help me with this question?

Let V be the vector space of all functions f : R → R and let T : V → V be a linear transformationsuch that T² f = 0 for all f ∈ V , where 0 denotes the constant zero function. Consider a transformationL : V → V defined by L(f) = T f − f.

(a) Show that f is a vector space.
(b) Show that L is linear.
(c) Show that L is injective.

Thanks

 

[pka]

Hello I have a maths midterm exam tomorrow and this question is from a tutorial I was absent on. Can any on help me with this question?
Let V be the vector space of all functions f : R → R and let T : V → V be a linear transformationsuch that T² f = 0 for all f ∈ V , where 0 denotes the constant zero function. Consider a transformationL : V → V defined by L(f) = T f − f.

(a) Show that f is a vector space.
(b) Show that L is linear.
(c) Show that L is injective.

May we see some work that you have done, please.
Also please review post for typos.

 

[stapel]

Hello I have a maths midterm exam tomorrow and this question is from a tutorial I was absent on.

Are you saying that you missed this material, and have yet to make it up, so you need to start with lesson instruction?