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Questions

If an SPL ( LINEAR EQUATION SYSTEM ) is known: Ax = b. A is a...

If an SPL ( LINEAR EQUATION SYSTEM ) is known: Ax = b. A is a matrix sized m × n and b is a vector sized m × 1, with the component values of matrix A and vector b known. The x vector is n × 1 and the component values are unknown. Explain how the possible solution of SPL Ax = b.

i want answer for the question , and what he mean by (the component values of matrix)

In: Advanced Math

S = Z (integers), R = {(a,b) : a = b mod 5}. Is this relation...

S = Z (integers), R = {(a,b) : a = b mod 5}. Is this relation an equivalence relation on S?

S = Z (integers), R = {(a,b) : a = b mod 3}. Is this relation an equivalence relation on S? If so, what are the equivalence classes?

In: Advanced Math

Reflect on the concept of exponential and logarithm functions. What concepts (only the names) did you...

Reflect on the concept of exponential and logarithm functions. What concepts (only the names) did you need to accommodate these new concepts in your mind? What are the simplest exponential and logarithmic functions with base b ≠ 1 you can imagine? In your day to day, is there any occurring fact that can be interpreted as exponential or logarithmic functions? What strategy are you using to get the graph of exponential or logarithmic functions? Provide a graph from Desmos graphing calculator of this function. Show your work.

In: Advanced Math

5. Find the general solution to the equation y'’ + 9y = 9sec2 3t

5. Find the general solution to the equation

y^'’ + 9y = 9sec² 3t

In: Advanced Math

How do you use mathmatical induction to show that the coefficient of x^2 in the expansion...

How do you use mathmatical induction to show that the coefficient of x^2 in the expansion of (1+x+x^2+...x^n)^n is (1+2+...n).

In: Advanced Math

using the Laplace transform solve the IVP y'' +4y= 3sin(t) y(0) =1 , y'(0) = -...

using the Laplace transform solve the IVP

y'' +4y= 3sin(t) y(0) =1 , y'(0) = - 1 , i am stuck on the partial fraction decomposition step. please explain the decomposition clearly.

In: Advanced Math

Find the distance between the skew lines with parametric equations x = 1 + t, y...

Find the distance between the skew lines with parametric equations x = 1 + t, y = 3 + 6t, z = 2t, and

x = 1 + 2s, y = 6 + 15s, z = −2 + 6s.

Find the equation of the line that passes through the points on the two lines where the shortest distance is measured.

In: Advanced Math

prove that a compact set is closed using the Heine - Borel theorem

In: Advanced Math

Given the following 40x40 matrix below, with starting vector V shown below also, apply the power...

Given the following 40x40 matrix below, with starting vector V shown below also, apply the power method to find the dominant eigenvalue of matrix using MATLAB program, MAPLE program or some other computer program to print out: the estimate of the lambda with tolerance 0.01, the number of iterations, and the converged lambda. Then print out the transpose of the eigenvector (should be 40 components) produced with up to two decimals.

Starting Vector V= [

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
];

Matrix A =

[

4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;

-1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;

0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 -1 4 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;

-1 0 0 0 0 0 0 0 0 0 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;

0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 0 0 0 0 0 0 0 0 0 -1;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 4 -1 0 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4 -1;

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 4;

]

In: Advanced Math

Write a short essay approximately 2 pages (for a first year engineering class).Introduce the concept of...

Write a short essay approximately 2 pages (for a first year engineering class).Introduce the concept of eigenvalues and eigenvectors including a short history of their development. Outline in detail some of the real life applications of the use of eigenvalues and eigenvectors in science, engineering and computer science, giving at least one example in each case. 10 Marks

In: Advanced Math

Provide an example 1) A nested sequence of closed, nonempty sets whose intersection is empty. 2)...

Provide an example

1) A nested sequence of closed, nonempty sets whose intersection is empty.
2) A set A that is not compact and an open set B such that A ∪ B is compact.

3) A set A that is not open, but removing one point from A produces an open set.

4) A set with infinitely many boundary points.

5) A closed set with exactly one boundary point

In: Advanced Math

Is there a difference between the means of occupancy rates in May and August? Answer your...

Is there a difference between the means of occupancy rates in May and August? Answer your question by calculating an approximate and appropriate symmetric 95% confidence interval using a Z statistic. Explain your findings

OR_MAY	OR_AUG
60	97
86	99
93	99
89	96
74	90
81	84
83	99
71	99
90	98
83	97
77	99
82	97
90	98
81	98
20	90
87	95
48	94
60	96
45	98
80	95
65	91
60	95
75	90
15	70
16	66
97	100
74	94
62	97
40	85
82	97
24	76
49	98
16	93
60	86
42	73
68	87
55	86
75	93
35	95
0	95
40	80
40	40
10	80
83	90
50	100
77	98
81	99
37	96
27	90
49	96
53	98
60	97
80	100
58	95
64	93
65	100
68	98
75	100
55	84
60	95
56	96
10	100
85	95
4	77
24	92
85	98
75	92
44	84
45	95
0	70
34	92
35	95
70	98
65	99
15	90
40	100
10	90
10	90
35	70
50	100
2	95
0	80
3	90
30	90
15	80
83	95
91	99
85	100
80	90
50	100
79	94
92	98
87	99
84	97
65	98
86	94
62	92
70	95
87	97
87	99
50	97
61	97
59	99
77	100
46	95
81	94
48	98
15	98
80	100
52	99
90	97
90	99
75	90
20	100
10	90
30	100
53	99
52	99
90	97
53	92
48	98
84	96
90	97
35	98
25	95
35	100
10	95
10	90
60	100
70	92
3	78
10	90
10	90
75	100
10	70

In: Advanced Math

The Chinese Remainder Theorem for Rings. Let R be a ring and I and J be...

The Chinese Remainder Theorem for Rings.

Let R be a ring and I and J be ideals in R such that I + J = R. (a) Show that for any r and s in R, the system of equations x ≡ r (mod I) x ≡ s (mod J) has a solution. (b) In addition, prove that any two solutions of the system are congruent modulo I ∩J. (c) Let I and J be ideals in a ring R such that I + J = R. Show that there exists a ring isomorphism R/(I ∩J) ∼ = R/I ×R/J.

In: Advanced Math

The length of the essay does not exceed 800 words in APA format Discuss the fundamentals...

The length of the essay does not exceed 800 words in APA format

Discuss the fundamentals of factorial design including main effects and interaction effect using a 2 × 2 factor design. Use your own hypothetical example for illustration.

In: Advanced Math

Solve the following LP using revised simplex algorithm in table format. Min 6x1+10x2 -18x3 +25x4 +15x5...

Solve the following LP using revised simplex algorithm in table format.

Min 6x1+10x2 -18x3 +25x4 +15x5

subject to 0.2x1+ 0.2x2+0.4x3+ 0.5x4 + x5 ≥ 1000

2.5x1+ 1.5x2+ x3 + 0.5x4 + 0.5x5 ≤ 1100

0.8x3 + x5 ≥ 500

x1, x2, x3, x4, x5 ≥ 0

In: Advanced Math