COT3100Hmk04 - determine a, b, c, and d in the expression...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
COT 3100 Fall 2002 Homework #4 Assigned: 10/8/02 Due: 10/22/02 in lecture 1) Use induction on n 1 to prove the following summation formula: . 9 ) 2 )( 1 3 ( 2 ) 2 ( 1 0 + = - + + - = - n n i i n i 2) Consider a sequence of numbers defined as follows: t(0) = 1, t(1) = 4, t(n) = 5t(n-1)-6t(n-2), for all integers n > 1. Prove for all non-negative integers n that t(n) = -2 n + 2(3) n . 3) Given two 2x2 matrices, mutliplication of these matrices is defined as follows: [ a b ] X [ e f ] = [ ae+bg af+bh ] [ c d ] [ g h ] [ ce+dg cf+dh ] Using this information, make a conjecture about the value of the expression below (ie.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: determine a, b, c, and d in the expression below, in terms of n) and prove your conjecture for all positive values of n using induction. n [ 1 0 ] = [ a b ] [ 1 1 ] [ c d ] (Note: this simply is asking you to find the matrix on the left raised to the nth power. Exponentiation with matrices is also repeated addition.) 4) Use induction to prove for all positive integers n that 1 2 2 + = < n n i i...
View Full Document

Ask a homework question - tutors are online