Let T: V- Wbe a linear transformation. Prove the following results. (a) N(T) = N(-T)

Question

Problem 6

Let T: V- Wbe a linear transformation. Prove the following results. (a) N(T) = N(-T). (b) N(Tfc) = N((-T)fc). (c) If V = W (so that T is a linear operator on V) and A is an eigenvalue of T, then for any positive integer k N((T-Alv)fc ) = N((Al v -T)f c ).

Answer 1

Step-by-Step Solution:

Step 1 of 3

L3 - 6 ex. Find the values of the other trigonometric functions if θ is in Quadrant IV and cosθ = . 2 3 Basic Trigonometric Identities 1) sin θ +c os 2 θ =1 2) tan θ +1=s ec 2θ 2 2 3) 1 + cot θ =c c θ 4) sin(−θ)= −sinθ 5) cos(−θ)=c os θ

Chapter 7.1, Problem 6 is Solved

Step 2 of 3

Step 3 of 3

Solution for problem 6 Chapter 7.1

Let T: V- Wbe a linear transformation. Prove the following results. (a) N(T) = N(-T)

Chapter 7.1, Problem 6 is Solved