Linear Algebra : Solving for Temperatures of Points on a Flat Square Plate

The concept of thermal resistance described in Problem 5 can be used to find the temperature distribution in the flat square plate shown in Figure 5(a). Figure 5(a) The plate's edges are insulated so that no heat can escape, except at two points where the edge temperature is heated to Ta and Tb, respectively. The temperat ...continues

Linear Algebra : Use Network Analysis to Determine Number of Traffic Sensors

A traffic engineer wants to know whether measurements of traffic flow entering and leaving a road network are sufficient to predict the traffic flow on each street in the network. Consider the network of one-way streets shown in the Figure 3. The numbers in the figure give the measured traffic flows in vehicles per hour. Assume ...continues

Linear Algebra : Cofactors and Inverse of Matrix

Find the cofactor of each element of A=[-1 1 2 3; 1 2 3 4; -1 1 -1 5; 1 -1 1 2] and also the inverse. I am having trouble with this 4 x 4 matrix.

Cyclic Vector

Suppose that T is a linear operator on a two dimensional vector space V, and that T is not multiple of the identity transformation. Show that T has a cyclic vector (i.e., there exists v V such that {v, Tv } is a base for V). Please see the attached file for the fully formatted problems.

Invertible Matrix, Linear Operator and One-to-one

Let A be an n invertible matrix. Define T: Mnm--> Mnm by T(B)A^-1 BA. i) Is T a linear operator? ii) Is T one-to-one?

Self-Adjoint Sets

4.1. If A, B are bounded operators on H, show that (AB)*= B*A*. Even if A, B are both self-adjoint, the product AB may not be.

Translation Operator : Adjoint and Inverse

4.6. Consider the translation operator Ta defined by Ta[U(x)] = u(x — a) on L2(-∞ ,∞). What is its adjoint? Its inverse?

Rates and Investments : Systems of Equations Problem

I would like to know if I am on the right track to writin this as a "systems of equations" using the substitution process. How much further do I have to go if this is right so far? A family made an investment for 1 year that earned $7.50 simple interest. If the principal had been $25 more and the interest rate 1% less, the in ...continues

Linear Programing/Simplex Method

A company makes product 1 and product 2 from two resources. The linear programming model for determining the amounts of product 1 and 2 to product (X1 and X2) is: maximize Z = 8X1 + 2X2 (profit, $) subject to 4X1 + 5X2 < 20 (resource 1, lb) 2X1 + 6X2 < 18 (resource 2, lb) X1, X2 > 00 I need to solve this ...continues

Linear Programning

A baby products firm produces a strained baby food containing liver and milk, each of which contribute protein and iron to the baby food. Each jar of baby food must have 36 milligrams of protein and 50 milligrams of iron. The company has developed the following linear programming model to determine the number of ounces of live ...continues