Find the least square of the system where and .
The solution .
Consider the system as follows.
where and .
Consider the matrix A as follows.
Now, find as follows.
The exact solution of the system is as follows.
After solving the matrix calculation as follows.
Then write the equation as follows.
Simplify further as follows.
Hence, the least square for the system is .
Leg traction. The accompanying figure shows how a leg may be stretched by a pulley line for therapeutic purposes. We denote by the vertical force of the weight. The string of the pulley line has the same tension everywhere. Hence, the forces role="math" localid="1659529616162" and have the same magnitude as . Assume that the magnitude of each force is 10 pounds. Find the angle so that the magnitude of the force exerted on the leg is 16 pounds. Round your answer to the nearest degree. (Adapted from E. Batschelet, Introduction to Mathematics for Life Scientists, Springer, 1979.)
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