Matrices (Matrix Product Rule); Geometric Series

1. Suppose that A = ... and C = ... (see attachment). Find a matrix for B such that AB = C or prove that no such matrix exists 2. Find the sum ... (see attachment)

Factoring

a. Convert (11101)2 to base 16. b. Use the Euclidean algorithm to find gcd(34,21).

Big-Oh Function

Please see the attached file for the fully formatted problems. I need to find the best big-oh function for the function. I need to choose my answer from among the following: 1, log2 n, n, n log2 n, n2, n3,…, 2n, n!. A. f(n) = 1 + 4 + 7 + ... + (3n + 1). B.

Big-Oh

Use the definition of the big-oh to prove that ... (see attachment)

Graphs and Their Representations

If all the nodes of a simple, connected, planar graph have degree 4 and the number of arcs is 12, into how many regions does it divide the plane?