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Linear Algebra

Prove Equalities

The following two questions I have trouble with: 1. Show that (1- x) n-1. x = (1-x)n-1 - (1-x)n 2. Prove that if ,  are the roots of the equation t² - 2t + 2 then: (x +) n - (x+) n / ( -) = sin n / sin n where cot  =

Linear Algebra

Determine q such that the system x + y + 2z = 3 2x -y - 3z = 2 x -2y -qz = 3 Has no solution

PDE : Complete solution to a non-linear equation.

The PDE is: xp + yq + p + q -pq = u which gives: p(x+1) + q(y+1) - pq - u = 0 Now, I need to find a complete solution. I have set up my characteristic system to be: dx /x+1-q = dy /y+1-p = du /u-pq = dp /p(pq-u-1) = dq /q(pq-u-1) Help! I cannot solve any of these integrals. I need p = P(x,y,u,a) and

Find the eigen values and eigen vectors of the matrix

Find the eigen values and eigen vectors of the matrix A = [9, -1 , 9; 3 , -1 , 3; -7 , 1 , -7] Also find the corresponding eigen spaces for the matrix A. Find a matrix B which reduce the given matrix A to the diagonal form by the transformation B^(-1)AB.

Characteristic equation of a matrix and inverse of a matrix

Linear Algebra Matrices Eigen Values and Eigen Vectors(I) Find the characteristic equation of the matrix A = [1, 3, 7; 4, 2, 3; 1, 2, 1] Show that the equation is satisfied by and hence obtain the inverse of the given matrix. The fully formatted problem is in the attached f

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.