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Linear Algebra

Mathematical modeling using systems of linear first order equations

Two tanks each hold 3 liters of salt water and are connected by two pipes (see figure below) the salt water in each tank is kept well stirred. Pure water flows into tank A at a rate of 5 liters per minute and the salt mixture exits tank B at the same rate. Salt water flows from tank A to tank B at the rate of 9 liters per min

Linear Algebra : Leontief Input-Output Model and Real-World Applications

1. Why did Leontief use linear algebra techniques to create his model? Can you think of alternative methods? 2. What are the main strengths of his model? 3. Does it have any limitations (that you can think of)? 4. How might the Input-Output model be useful in the real world? (In other words, would anyone except an Economist

Mathematical System

I am having a problem drawing the table for the following system: Define a universal set U as the set of counting numbers. Form a new set that contains all possible subsets of U. This new set of subsets together with the operation of set intersection forms a mathematical system. Then I have to tell which properties that we did

Subsets in n-space

I've been having trouble with this and need some assistance. v - union ^ - intersection If S and T are subsets of Rn, prove that (int S) ^ (int T) = int (S^T) and (int S) v (int T) subset int(SvT)

Systems of Equations Application and Systems of Inequalities

# 41 Nickels and dimes. Windborne has 35 coins consisting of dimes and nickels. If the value of his coins is # 3.30, then how many of each type does he have? # 43 Blending fudges. The chocolate factory in Vancouver blends its double-dark-chocolate fudge, which is 35% fat, with its peanut butter fudge, which is 25% fat, to

Systems of Linear Equations : Row Operations and Solutions

1. Find the augmented matrix for each system of linear equations: a. 5x1 + 7x2 + 8x3 = 3 -2x1 + 4x2 + 9x3 = 3 3x1 - 6x2 + x3 = 1 b. 4x1 + x2 - 7x3 = 6 5x1 + 7x2 + 2x3 = 3 5x1 + 2x2 + 5x3 = 7 c. 3x1 - 2x2 + 2x3 = 7 5x1 + 7x2 + 3x3 = 3 -5x1 + 6x2 - 8x3 = -5 2. Using elementary row operations reduce each of the augm

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

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.

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

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

Matrix Representation of a Linear Operator on Vector Space

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.