### Pre Algebra Equations

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1. A small school held a fund raiser. A total of 23 adults and children attended. Each adult paid $10, and each child paid $2 to attend. If a total of $86 was raised, use a system of equations to determine how many adults and how many children attended. Solve the system using Gaussian Elimination. 2. Two zinc alloys cont

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Can I please find out what I am doing incorrectly with the following problem? "I have seventy five coins in my pocket made up of quarters and dimes. If the total value of the coins is $12.45, how many of each coin do I have?" q + d = 75 Let q represent quarters (0.25)q + (0.10)d = 12

Write a system of equations and then solve the following using matrix inverses. Consider a company that specializes in gourmet chocolate baked goods-chocolate muffins, cookies and brownies. Each chocolate muffin requires 2 units of chocolate, 3 units of flour and 2 units of sugar. Each chocolate cookie requires 1 unit of c

Let a_1, ..., a_n be distinct real numbers. Prove that the functions U_i(x) = exp (a_i x) are independent.

P7 Solve problems involving expansion. Task 1: A steam pipe has a length of 20 m at 20 degrees C. If the coefficient of linear expansion is 0.000012 /K. How much expansion will have to be allowed for when the steam increases the temperature of the pipe to 300°C? Task 2: A copper sphere has a diameter of 40 mm at 0 degrees C.

Several state and federal government spokespersons who use linear equations in a variety of ways. 1. An employee of the National Parks Service told you about a location in Washington, DC. It is a large grassy area south of the White House known as the Ellipse. The National Tree Lighting Ceremony is held annually on the Ellipse

Let A be a 7x7 matrix. Find all solutions of the equation A^7 = 0 up to conjugacy.

Let L(A) = A + A^t be a map on the space of all 5x5 symmetric matrices. Prove that L is a linear operator and find its matrix in some basis.

27. Solve the system of linear equations by the addition method. 2x + 6y = 2 3x - 6y = 33

14. Solve using a linear equation with a work check at the end :A plumber charged a customer $117, listing $47 for materials and the rest for labor. If the plumber charged for 2 hours, what is the hourly rate for labor?

28.Use linear equation with a work check at end. An appliance store buys 6 washers and 5 dryers at a total cost of $1949. Another appliance store buys 4 washers and 5 dryers from the same wholesale supplier at a total cost of $1561. Find the cost of one washer and one dryer.

A manufacturer finds that the cost y of producing x units is given by the formula of the form y=mx+b. If it costs $1300 to produce 20 units and $1750 to produce 35 units, what is the fixed cost?

Please discuss the following: - Explain why vectors QR and RQ are not equivalent. - Explain when the elimination method for solving a system of equations is preferable to the substitution method. Give examples.

Factorize 513833.

1) Let A be a linear operator on n-dimensional vector space V if {see attachment}. For some {see attachment}, prove that matrix representation {see attachment} of A with respect to a basis ... Please see attachment for complete question.

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!