Eigenvalues, EigenVectors

(See attached file for full problem description)

Linear algebra

Please help in solving the problem attached using linear algebra to solve for the currents.

Linear algebra

(See attached file for full problem description with diagrams) --- Engineers use the concept of thermal resistance R to predict the rate of heat loss through a building wall in order to determine the heating system's requirements. This concept relates the heat flow rate q through a material to the temperature difference ∆T across the material: q = . This relation is like the voltage-current relation for an electrical resistor: i = . So the heat flow rate plays the role of electrical current, and the temperature difference plays the role of the voltage difference v. The SI unit for q is watt/meter2. A watt is 1 joule/second. The wall shown in Figure 4(a) consists of fou... click for more

Linear algebra

(See attached file for full problem description with diagrams and symbols) --- 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 temperature varies through the plate, so no single point can describe the plate's temperature. One way to estimate the temperature distribution is to imagine that the plate consists of four sub-squares and to compute the temperature in each sub-square. Let R be the thermal resistance of the mat... click for more

linear algebra

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 that no vehicles park anywhere within the network. If possible, calculate the traffic flows f1 through f7. If not, determine how many more traffic sensors need to be installed (within the network) and obtain the expressions for the other traffic flows in terms of the measured quantities.