Questions
For all n > 2 except n = 6, show how to arrange the numbers 1,2,...,n2...

For all n > 2 except n = 6, show how to arrange the numbers 1,2,...,n2 in an n x n array so that each row and column sum to the same constant.

In: Advanced Math

Find the first four terms of the sequence (an)n≥1 with the given definition. Determine if they...

Find the first four terms of the sequence (an)n≥1 with the given definition. Determine if they are potentially arithmetic or geometric.

(a) an is the number of n-bit strings which have more 1’s than 0’s. (Also, write down the strings for n ≤ 4.)

(b) an is the number of n-bit strings in which the number of 1’s is greater than or equal to the number of 0’s in every prefix. For example, 010111 would not qualify, since the prefix 010 has more 0’s than 1’s. (Also, write down the strings for n ≤ 4.)

(c) an is the number of lattice paths from (0, 0) to (n, n). (Refer to Section 1.2 if you need a refresher on lattice paths.)

In: Advanced Math

et A be a 157 x 157 upper-triangular matrix. Suppose that every diagonal entry of A...

et A be a 157 x 157 upper-triangular matrix. Suppose that every diagonal entry of A is 1 and that there is at least one nonzero off-diagonal entry in A. Is A diagonalizable? Explain how you can answer this question mentally, with no non-trivial calculations.

In: Advanced Math

Which of the following sets are closed under addition? (i) The set of all vectors in...

Which of the following sets are closed under addition?

(i) The set of all vectors in R2 of the form (a, b) where b = a2.
(ii) The set of all 3 × 3 matrices that have the vector [3 -1 -1]T as an eigenvector.
(iii) The set of all polynomials in P2 of the form a0 + a1 x + a2 x2 where a0 = a2.
(A) (i) only (B) all of them (C) (ii) only (D) (i) and (iii) only (E) (iii) only (F) none of them (G) (ii) and (iii) only (H) (i) and (ii) only

In: Advanced Math

1. a) A monic polynomial is a polynomial which has leading coefficient 1. Find the real,...

1.
a) A monic polynomial is a polynomial which has leading coefficient 1. Find the real, monic polynomial of the lowest possible degree which has zeros −1−i,−2i and 3i, and z is the variable.
b) i) If we prove that if a, b and c are integers such that a|b and a|c then a|(b + c), what is the converse of this statement, and is it true?
ii) Why is the statment “If it is Thursday, then I have a pasta for dinner. Today is Friday, so I will not have a pasta for dinner” not valid?

In: Advanced Math

Let L1 be the line passing through the point P1=(−3, −1, 1) with direction vector →d1=[1, −2, −1]T, and let L2 be the line passing through the...

Let L1 be the line passing through the point P1=(−3, −1, 1) with direction vector →d1=[1, −2, −1]T, and let L2 be the line passing through the point P2=(8, −3, 1) with direction vector →d2=[−1, 0, 2]T.
Find the shortest distance d between these two lines, and find a point Q1 on L1 and a point Q2 on L2 so that d(Q1,Q2) = d. Use the square root symbol '√' where needed to give an exact value for your answer.

d = 

Q1 =
Q2 =

In: Advanced Math

Let A be a set with m elements and B a set of n elements, where...

Let A be a set with m elements and B a set of n elements, where m; n are positive integers. Find the number of one-to-one functions from A to B.

In: Advanced Math

Convert to standard maximum form and apply two iterations of simplex process using slack form. Maximize...

Convert to standard maximum form and apply two iterations of simplex process using slack form.

Maximize

2x1 -6x3

Subject to

x1 + x2 – x3 <= 7

3x1 – x2 >= 8

-x1 + 2x2 + 2x3 >= -2

x2, x3 >=0

Please write the answer very clearly.

In: Advanced Math

Question: Respond to these 2 posts explaining the reason for your agreement or disagreement or why...

Question: Respond to these 2 posts explaining the reason for your agreement or disagreement or why you thin...
Respond to these 2 posts explaining the reason for your agreement or disagreement or why you think the post is important, and/or providing examples of the point(s) made. A couple sentences are acceptable.

Post 1:

The first step in determining the maximum or minimum value of a quadratic polynomial is to analyze the polynomial and determine if the parabola opens upward or downward. You would then find the vertex, followed by the x-intercept, followed by the y-intercept. Once you've found that information, you can sketch the the function on a graph. You'll determine the axis of symmetry and then after doing that you will be able to locate the maximum and minimum values of the quadratic polynomial.

Post 2:

If you have a>0 then your y coordinate of the vertex opens upward so its a minimum, it will also be a minimum if your quadratic equation is positive you can also find the minimum by graphing the function.

If you have a<0 then your vertex opens downward and you have a maximum, or you can use the equations -b/2a to find the x coordinate of the vertex , this equation can be used to find either the Minimum or Maximum.

In: Advanced Math

Find general solutions of the following systems using undetermined coefficients. X′ =(2x2 matrix) ( 2 2;...

Find general solutions of the following systems using undetermined coefficients.

X′ =(2x2 matrix) ( 2 2; 3 1 ) X + (column matrix) ( e^−4t; 0 )

In: Advanced Math

certain birth defects and syndromes are polygenetic in nature. typically , fhe chance that an offspring...

certain birth defects and syndromes are polygenetic in nature. typically , fhe chance that an offspring will be born with polygenetic affilction is small. however once the offspring is born with fhe afflixtion , the probability of the same offspring of the same parents will be born eith same affliction increases. lets assume thst the probability of the child being born eith affixtion A is .002. if a child is born with this , the probability of a future child beinf born of a future child with same afflixtion become .08.

1.are the events of the birth of 2 children in fhe same familg with affliction A independent?

2. a couple plans to have one child. determime probability that the child will be born with this affiction.

3. another couple plans to have 2 children . determine rhe probability that both children will be born with the afffixtion.

4 . determine the probability that the first wil be born with affixfion and second wont

In: Advanced Math

1. Find general solutions of the following systems using undetermined coefficients. a.) x′ = −5x +...

1. Find general solutions of the following systems using undetermined coefficients.

a.) x′ = −5x + 6y + 1

y′ = −7y + t .

b.) x′ = 6x − 5y + e^5t

y′ = x + 4y .

c.) x′ = −6x − 3y + te^2t

y′ = 4x + y .

In: Advanced Math

Consider the function, ? (?) = 20?² + 28? - 17 Determine both real roots of...

Consider the function, ? (?) = 20?² + 28? - 17

Determine both real roots of the quadratic equation as follows:

i. Graphically and determine the intervals for both roots to be used in iii & iv.

ii. Using the quadratic formula

iii. Using the bisection method until ?? is less than ?? = 0.5%

iv. Using the false-position method until ?? is less than ?? = 0.5%

In: Advanced Math

Let A be such that its only right ideals are {¯0} (neutral element) and A. Show...

Let A be such that its only right ideals are {¯0} (neutral element) and A. Show that A or is a ring with division or
A is a ring with a prime number of elements in which a · b = 0 for any, b ∈ A.

In: Advanced Math

Approximately how many flops are needed to find the LU factorization of an n x n...

Approximately how many flops are needed to find the LU factorization of an n x n matrix using Doolittle’s method? If a computer requires 1 second to find an LU factorization of a 500 x 500 matrix, what would you estimate is the largest matrix that could be factored in less than 1 hour?

In: Advanced Math