Category Archive for: Linear Algebric Equations

An Overdetermined Set

An Overdetermined Set (a) Solve the following equations by hand and (b) solve them using MATLAB. Discuss the solution for two cases: c = 9 and c = 10. x+y=1 x + 2)’ = 3 x +5y = c • Solution (a) To solve these equations by hand, subtract the first equation from the second to…

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The Least Squares Method

The Least Squares Method Suppose we have the following three data points, and we want to find the straight line Y = mx +b that best fits the data in some sense. (a) Find the coefficients m and b by using the least squares criterion. (b) Find the coefficients by using MATLAB to solve the three…

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Traffic Engineering

Traffic Engineering 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. For example, consider the network of one-way streets shown in Figure 6.4-2. The numbers in the figure give the measured traffic flows in vehicles per hour.…

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Production Planning

Production Planning The following table shows how many hours-reactors A and B need to produce I ton each of the chemical products I, 2, and 3. The two reactors are available for 40 hours and 30 hours per week, respectively. Determine how many tons of each product can be-produced each week. • Solution Let x, y, and z…

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A singuler Set

A singuler Set The following underdetermined equation set was analyzed in Example 6.4-2. There it was shown that an infinite number of solutions exists. Use the pinv and the rref commands to obtain solutions. 2x-4y+5z=-4 -4x – 2} + 3z = 4 2x + 6)’ – 8;: == 0 • Solution First use the p i nv…

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EXAMPLE

A Statically Indetenninate Problem Determine the forces in the three equally spaced supports that hold up a light fixture. The. supports are 5 ft apart. The fixture weighs 400 lb, and its mass center is 4 ft from the right end. (a) Solve the problem by hand. (b) Obtain the solution using the MATLAB left-division method and the…

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An Underdetermined Set

An Underdetermined Set Show that the following set does not have a unique solution. How many of the unknowns will be undetermined? Interpret the results given by the left-division method. 2x ~ 4y +Sz = -4 4x – 2y +3z = 4 2x +6y – Sz = 0 • Solution A MATLAB session to check the…

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A Set Having a Unique Solution

A Set Having a Unique Solution Determine whether the following set has a unique solution, and if so, find it: 3x – 2y + 8z = 48 – -6x+5y+i=-12 9x + 4y + 2z = 24 ans = 3 »rank ([A b)) ans 3 »x A\b x 2 -1 5 Because A and [A b]…

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The Matrix Inverse Method

The Matrix Inverse Method Solve the following equations using the matrix inverse: 2x +9y = 5 3x – 4y:;:: 7

Calculation of Cable Tension

Calculation of Cable Tension A mass m is suspended by three cables attached at the three points B, C, and D, as shown in Figure 6.2-2; Let TI’ T2, and T3 be the tensions in the three cables AB, AC, and AD. respectively. If the mass m is stationary, the sum of the tension components in the…

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