full step plx

2. For each positive integer in1 let An be the following 11 x 11 matrix: b l 0 0 0 0 0 0 l b 1 0 0 0 0 0 0 l b l 0 0 0 0 0 0 1 b 0 0 U 0 0 0 0 0 b l 0 0 0 0 0 0 l b l 0 0 0 0 0 1 b l D 0 0 0 I} 0 l b where b E R' That is: [A3]\" = b {01' 1 S i S 11: [Auk-.34.] =1 for l 3;," S n l: [Aalk+l.k=l forlskSn-l; [Aalig'=0 ifiajandjaiztl. Lot on = detMm). (3) Express al, 02 in terms of b. (b) Show that an.\" ban + and = l} for each n 2 2. (c) (i) Suppose I) 96 i2. Let :11 6 he the roots of the quadratic polynomial .172 bx + 1. (Since b at i2, or 75 3-) Apply mathematical induction to show that a1; = (Hint: Take the proposition P(n) as mathematical induction is to be applied.) (ii) Suppose b = 2. Compute on for each positive integer n. (Hint: Consider on+1 an.)