Exercises 19–23 concern the polynomial and an n × n matrix Cp called the companion matrix of p: Let p be the polynomial in Exercise 22, and suppose the equation p(t) = 0 has distinct roots . Let V be the Vandermonde matrix (The transpose of V was considered in Supplementary Exercise 11 in Chapter 2.) Use Exercise 22 and a theorem from this chapter to deduce that V is invertible (but do not compute V –1) Then explain why V–1 CpV is a diagonal matrix.Reference Exercise 22:Exercises 19–23 concern the polynomial and an n × n matrix Cp called the companion matrix of p: a. Write the companion matrix for p. and show that is an eigenvector of the companion matrix for p.

Chapter 4: ExercisePhysiology Energy and Work Immediate energy sources o 1-5 seconds o ATP, PC o Anaerobic Short term energy sources o <2 min o Glycolysis (breakdown of CHO) o Anaerobic Long term energy sources o >2 minutes o Muscleglycogen, glucose,plasma FFA o Aerobic ATP Production Anaerobic exercisedecreases %of ATP production with more time Aerobic exerciseincreases %of ATP production with more time MuscleFiber Types: Genetics,Sex, Training Distribution has a wide variation Genetic component (fraternal twins) Fast-twitch fibers do not convert to slow-twitch with training Training increases oxidative capacity