Plot them then take a picture
Answer:
See explanation and proof below.
Step-by-step explanation:
For this case we want to proof the following:
"Given that V is a finite dimensional and then ST is invertible if and only if S and T are both invertible.
In order to proof this we need to use the following result :"Given a finite dimensional vector space V, for any T \in L(V,V) we have the following properties defined: "invertibility, surjectivity, injectivity".
Proof
(> statement)
For the first part of the proof we can do this. We assume two vectors in V. If we assume that ST is invertible and then we have this :
And since ST is invertible then and that implies that T is invertible.
Now if we select a vector b in V , since we know that ST is invertible, and by the surjective property defined above we have that for any then and we see that and S is surjective and by the result above is invertible.
(< statement)
Now for this part we can assume that S and T are invertible and then for any two vectors . Since S,T are invertible and using the surjective property we have that for any vectors we have that:
And since and because S satisfy the injectivity property that implies:
and we can conclude that and the conclusion is that ST is injective and invertible for this case.
And with that we complete the proof.
Answer:
Elevator 1 is 16 feet above ground level, and elevator 2 is 25 feet below ground level
Step-by-step explanation:
Elevator one is moving up, so it means it's above ground level since it started on the ground
Elevator is moving negative floors, so it is moving below.
Let me know if you have any questions!
Answer:
Option F.
Step-by-step explanation:
we know that
The circumference of a circle is equal to
in this problem
substitute
-----> exact value of the circumference
Find the approximate value of the circumference
assume