Row Equivalent Matrices and Systems of Equations

Determine the solutions of the system of equations whose matrix is row-equivalent to: Give three examples of the solutions. Verify that your solutions satisfy the original system of equations. Show work.

Solving Systems of Equations with Three Variables

Solve the following systems of equations: x1 + x2 = 1 -x1 + x2 + x3 = -1 -1x2 + x3 = 3 -Show all necessary work.

Matrix Inverses

Show that: (Matrix) 2 3 -1 1 2 1 -1 –1 3 is the inverse of 7 -8 5 -4 5 3 1 -1 1 Show all work.

Proof by Induction : Step-by-step

Let p(n) be the statement that: 1^3 + 2^3 + ... + n^3 = (n (n + 1) /2)^2 for the positive integer n. a) What is the statement P(1)? b) Show that P(1) is true, completing the basis step of the proof. c) What is the inductive hypothesis? d) What do you need to prove in the inductive step? e) Complete the inductive ...continues

Probability Game of Shooting

In a single duel, Shooter A hits target with a probability of 1/3. B with 1/2. C never misses. ABC fire in turns, A going first, B next, and C last. Shooting cycle repeats until only one dueler has not been hit. Use random # x, where 0 <= x <=1. What happens if the shooter hits the deadliest shooter first? in 10,000 du ...continues

Bit Strings

(a) How many bit strings of length 6 are there? Explain fully. (b) How many bit strings of length 6 are there which begin with a 0 and end with a 0? Explain fully. (c) How many bit strings of length 6 start with a 0 bit or end with a 0 bit? Explain fully.

Combinations

A women has 9 close friends. (a) In how many ways can she invite five of these to dinner? Explain/Show work. (b) Repeat part (a) with the added stipulation that two of her friends do not like each other so that if she invites one of them she cannot invite the other. Explain/Show work. (c) Repeat part (a), assuming ...continues

Binomial theorem and expanding a polynomial

Use the Binomial Theorem to write the expansion of (x + y)^6

Haase Diagrams and Partial Ordering Relations

Consider the following Hasse diagram of a partial ordering relation R on a set A: (a) List the ordered pairs that belong to the relation. (b) Find the (boolean) matrix of the relation. See attached file for full problem description.

Matrices, Sets and Relations

Let: D = days of the week {M, T, W, R, F}, E = {Brian (B), Jim (J), Karen (K)} be the employees of a tutoring center at a University U = {Courses the tutoring center needs tutors for} = {Calculus I (I), Calculus II (II), Calculus III (III), Computers I (C1), Computers II (C2), Precalculus (P)}. We define the relatio ...continues