Explain why a 2 x 2 matrix can have at most two distinct eigenvalues. Explain why an n x n matrix can have at most n distinct eigenvalues.

Use the inverse of the function y=x^2-18x to find the unknown value [tex]y = \sqrt{bx + c \: + d} [/tex]

What is the range of the relation in the table below? x y –2 0 –1 2 0 4 1 2 2 0

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .