### System of Equations Word Problem : Sum and Product of Two Numbers

Find two numbers whose product is 192 and the sum of the first plus three times the second is a minimum. (There should be and easily identifiable primary and secondary equations)

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Find two numbers whose product is 192 and the sum of the first plus three times the second is a minimum. (There should be and easily identifiable primary and secondary equations)

A rectangle window is framed by two rectangular shutters. The window is twice as tall as it is wide. The shutters are as tall as the window, and their widths are 24 cm less than their heights. The combined areas of the shutters total the same as the area of the window. Find the heights. The combined areas of the shutters total t

1. a) Consider the problem of cubic polynomial interpolation p(xi) = yi, I = 0,1,23 with deg(p) ≤ 3 and x0, x1, x2, x3 distinct. Convert the problem of finding p(x) to another problem involving the solution of a system of linear equations. b) Express the system from (a) in the form Ax = b, i

Hello. I'm trying to do a principle component analysis of the following file of "good values" - to create a good data signature. I need to find the eigenvectors of each data series. How do I derive the eigenvalues (or eigenvectors) and what are they from this data set? (If you could explain how to do it in matlab, that wo

Suppose that the random variables X1, X2 and X3 have the covariance matrix... (i) Determine the three PC's based on ∑. (ii) What percentage of the total variation is explained by each of the PC's (iii) Calculate the correlation coefficients between the first PC and each of the variables X1, X2 and X3. (iv) What are the

Consider the following (3x3) matrix A... Find the eigenvalues and eigenvectors of A and hence its spectral decomposition. Hence find... Please see attached for full question.

Let R={[a 0] | a,c,d ε Z } and define I={[m 0] | m,n ε Z}. [c d] [n 0] (ii) Is I an ideal in M2(Z)={[a b] | a,b,c,d ε Z}? Why or why not? [c d] I did part (i). So, I only need help on part (ii) Please see attached for

Problem 8.1 (Prob. 11, p.251) Solve the following system of equations. { x' = y { y' = -x Problem 8.2 (Prob. 18, p.251) Solve the following system of equations with given initial conditions. { x' = -y { y' = 10x - 7y { x(0) = 2 { y(0) = -7

Solve: 2X + Y = 8 4X + 10Y = 20 Find slope: A ( 4, 6) B (2,3)

Functional Analysis Normed Linear Space

Determine the length of pipe that a gas company will need to connect a house which is situated at the point (-6,8) to a gas line whose equation is y=-3x+2.

1) Which of the following equations describe the same line as the equation 3x+ 4y =5? a. y = (3/4)x + 5 b. 6x + 8y = 5 c. y = (3/4)x + 5/4 d. 5 - 3x - 4y = 0 e. none of the above 2) The equation of the vertical line passing through (-3,5) is a. x = -3 b. x = 5 c. y = -3 d. y = 5 e. none of the above 3)

Suppose that E is a normed linear space. Prove that if E* is separable, then E is separable. **See attachment for complete problem. Thanks!

Suppose that is a Banach space over K. A subspace M of is said to be complemented in if there exists a subspace N of such that =M N, that is if , then there exists in M and in N such that , and M N . Prove that each finite dimensional subspace of is complemented in . Hint: Suppose that M is a finite dimens

An electron is accelerated in a linear particle accelerator. At time t = 0, its speed is v0 along the axis of the accelerator, and it is subjected to a force producing a constant acceleration of magnitude a. Select the option which represents the formula most appropriate for finding the distance s that the electron has travel

I must solve the following linear equations using matrix methods. x+y-z=-8 3x-y+z=-4 -x+2y+2z=21 I am trying to understand the method of solving for variables of linear equation by forming them into a matrix and solving for the variables. Please help.

Let A = {see attachment} a. Solve x' = Ax b. Solve x' = Ax subject to x(0) = 0

Subject to the conditions x(0) = 0 and y(0) - 1, completely solve the following system of differential equations: x' = x y' = xy + e^t

(x^2 - x + 1)y" - (x^2 + x)y' + (x + 1)y = 0

Please solve the attached problems on bounded linear operators and bounded invertible equations.

Solve for x(1), x(2), x(3); 1. 27,954.606 x(1) + 11,969.843 x(2) - 7515.1688 x(3) = 6124.3394 2. 11,969.843 x(1) + 5900.332 x(2) - 3586.4121 x(3) = 3054.3092 3. -7515.1688 x(1) - 3586.4121 x(2) + 2513.4532 x(3) = -1756.4525

A-Solve: 4x=3y-6 4y=3x+1 b-Solve: 3x+4y=8 y=-3x+2

Let p be a prime in Z. Define Z(p) = {m/n in rational Q | p does not divide n} i) Show that Z(p) is a subdomain of Q ii) Find the units in Z(p) ,

1) Let { 1, 2, 2........... n} be a basis of an n dimensional vector space over R and A be n Matrix . Let ( 1, 2, 3............... s) = ( 1, 2, 2........... n) A Prove that dim (span { 1, 2, 3............... s}) = Rank (A). 2) Let V1 be the solution space of x1 +x2 + x3............+xn = 0 let V2 be the solution spac

.....is a commutative diagram of groups and that the rows are exact,... being homomorphisms. Prove that (a) if and are surjections and is an injection, then is an injection. (b) if , and are injections, then is an injection. 2. For a group extension {e} B H G {e} Prove that G ~ H/ (B).

See attachment for question. 1 Suppose that  is a finite dimensional normed linear space. a) Let be a basis for . Define Prove that 1, the closed unit ball in , is compact in (, ) b) Prove that any two norms on  are equivalent.

Suppose that N is a normed linear space. Prove that each finite dimensional linear submanifold of N is complete and therefore closed.

1. Let G be a group and H be a subgroup of G of index equal to 2. Prove that H G 2. Let (G,?) be a group and H G. Prove that if G/H is a p-group and is a p-group then is a p-group H. Please see the attached file for the fully formatted problems.

Given a 3x3 matrix M whose individual rows add up to 1 find a 3x1 vector v (not all zero) such that v=Mv. (Hint: Do a few examples.)

An event F is said to carry negative information about an event E, and we write.... Prove or give counterexamples to the following assertions... (See attachment for full question)