Solution Found!
For Exercises 2 through 6, prove that T is a linear transformation, and find bases for
Chapter 2, Problem 2(choose chapter or problem)
For Exercises 2 through 6, prove that T is a linear transformation, and find bases for both N(T) and R(T). Then compute the nullity and rank of T, and verify the dimension theorem. Finally, use the appropriate theorems in this section to determine whether T is one-to-one or onto.
Questions & Answers
QUESTION:
For Exercises 2 through 6, prove that T is a linear transformation, and find bases for both N(T) and R(T). Then compute the nullity and rank of T, and verify the dimension theorem. Finally, use the appropriate theorems in this section to determine whether T is one-to-one or onto.
ANSWER:Step 1 of 4
Given:
First, to prove that is a linear transformation.
Let and.
Further solving,
Therefore, is a linear transformation.