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Linear Algebra

Systems of Equations and Linear Programming : Six Word Problems

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

System of Equations Application Word Problem : Quarters and Dimes

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

Expansion of Pipes and Spheres Given the Coefficient of Linear Expansion

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.

Equation of an Ellipse, Interest and Lotto Probability

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

Linear Equation Application Word Problem

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?

System of Equations Application Word Problem

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.

System of Equations Application Word Problem

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

Cubic polynomial interpolation

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

Linear algebra: finding eigenvalues

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

Multivariate Statistics

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

Multivariate Statistics

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.

Ideals

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

Systems of Ordinary Differential Equations (4 Problems)

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

Linear Equations, Subsets, Interest and Probability (14 Problems)

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)