Text: Gilbert Strang. Introduction to Applied Mathematics.

First assignment. Due Monday, August 30.

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Challenge!
Crossing a plain, tourists have lost their way in a mist. Suddenly, they find a message at a fallen pole that reads: "A straight road is within a mile from that pole." The direction to the road is lost because the pole is fallen. The tourists need to find the road exploring the plain around. They are shortsighted in the mist: They can see the road only when they step on it.
What is the shortest way to the road even if the road is most unfortunately located?

Generate a square matrix A with random entries, each entry is from the interval [0, 1]. Compute the determinant of such matrix. Take the order of the matrix equal to 2, 5, 10, 15. Compute the norm of the solution of the equation A x=b. Discuss the results.

What is the range of determinants of matrices with entries from the interval [0, 1]. Take the rank equal to two and three.