1. Let x₁ = 2, and define

(a) Show that is always greater than or equal to 2, and then use this toprove that x_n? x_n+1? 0. Conclude that

(b) Modify the sequence (x_n) so that it converges to .

2. Let S : Rp --> Rn and T : Rn --> Rm be linear transformations. Show that the mapping x --> T(S(x)) is a linear transformation from Rp to Rm. Justify each step and explain why this computation gives the desired conclusion.