Linear Algebra

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Linear Algebra : Gaussian Elimination

X + y + 2x = 3 2x - y - 3z = 2 x -2y - z =3 Solve using Gauss method

System of Equations: Two Variables

Solve y = .5x y + 6 = .75(x+6).

Linear algebra system of equations

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

System of Equations and Linear Programming : Solving Subject to Constraints

1. Solve the following system of simultaneous equations: 6x1 + 4x2 = 40 2x1 + 3x2 = 20 x1 = ??? put your answer in the form x or x.x 2. Max Z = 5x1 + 3x2 Subject to: 6x1 + 2x2 <= 18 15x1 + 20x2 <= 60 x1 , x2 >= 0 Find the optimal profit. Z=? put your answer in the form x.xxx 3. Consider the

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

System of Equations Application Word Problem

A merchant mixed 10 lb of cinnamon tea with 5 lb of spice tea. The 15 pound mixture sells for $40. A second mixture includes 12 lb of cinn tea and 8 lbs of spice tea. The 20 lbs mixture sells for $54. Find the cost per lb of the cinn tea and the spice tea.

20 Systems of Equations Problems : Gauss-Jordan, Matrix Inverses, Production Matrices, Echelon Method and Application Word Porblems

(See attached file for full problem description) --- 1. What is true about the number of solutions to a system of m linear equations in n unknowns if m = n? If m < n? If m > n? Solve each system by the echelon method. 3. 2x + 3y = 10 -3x + y = 18 5. 2x - 3y + z = -5 x + 4y + 2z = 13 5x + 5y + 3z = 14 S

To show that a given matrix is idempotent

Linear Algebra Matrices (X) Idempotent of a Matrix Show that the matrix A = [2, -1 , 1; -2 , 3 , -2; -4 , 4 , -3]

To show a given matrix is orthogonal

Linear Algebra Matrices (IX) Orthoganal Matrix Show that the matrix A = [-8/9, 4/9 , 1/9; 1/9 , 4/9 , -8/9; 4/9

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.

Estimate the linear trend equation for the production series

Estimate line and find linear trend equation of the attached. A. Estimate the linear trend equation for the production series by drawing a line through the data. B. What is the average annual decrease in production? C. Based in the trend equation, what is the forecast for the year 2005? (See attached file for full pr

Advanced Linear Algebra : Nilpotent, Vectors, Basis and Linear Independence

Let T: IR^3 IR^3 , T(x,y,z) = (o,x,2y) - Show that T is nilpotent of index 3 (that is, T^3 = 0 and T^2 different from 0 ) - Find a vector v E IR^3 s.t T^2(v) different from 0 and show that B = { v, T(v), T^2(v) } is linearly independent (so basis) - Find A = [ T ] an

Computer Applications & Substitution, Elimination and Matrices

What computer applications can be used to graph systems of equations? Have you ever personally used any applications to graph an equation? In what circumstances does it make more sense to graph a system than to use the substitution, elimination, or matrix methods?

Advanced Linear Algebra : Transformations, Basis and Eigenvalues

(See attached file for complete problem description) --- Let T: IR^3 IR^3 T(x,y,z) = (y+z, x+z, y+x) B1 = standard basis of IR^3 and B2 the basis B2 = {u1= (1,1,1), u2 = (1, -1,0), u3 = (1,1,-2)} - Find A= [ T ] , B = [ T ] B1

Systems of Equations : Supply and Demand Equatons, Gaussian Elimination and Computer Applications

1) Solve the following system of equations that model supply and demand for a product: p - q = 0 ( supply equation ) cp - q = -1 ( demand equation ) where p = price and q = quantity Solve first when c = 0.999 and a second time when c = 1.001. What does the difference in solutions suggest about t

Isotherms

Please show each step of your solution. When you use theorems, definitions, etc., please include in your answer. If there is anything unclear in the problem, let me know. Thank you. Solve for u(r, O) and sketch, based on intuition... (See attachment for full problem)

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

Pre Algebra Equations

Please see attachment. Thank you very much!

Systems of Equations and Linear Programming: Six Word Problems

See the attached file. 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.

Solutions of the system of equations

Determine the solutions of the system of equations whose matrix is row equivalent to 1 0 −1 |1 0 1 3 |1 0 0 0 |0 Give three examples of the solutions. Verify that your solutions satisfy the original system of equations.

Linear Prgramming and Simplex Solutions

See attachment for problem.

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

Word Problems as Systems of Equations and Solving the Systems

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

Proof of the linear independence of exponential functions.

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

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

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