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MATH 271 (Linear Algebra II)

Final Evaluation Questions (MATH 271)

Questions for the Written Report (Submit the written report in Microsoft Teams as one PDF document)

1. Let S 2   = {(x, y)x 2  + y 2   = 1}. Define the operation of addition on this set by taking (x, y)+ (u, v) = (xu − yv, xv + yu) . Prove that  S 2 is closed under this operation. (10 points)

2. Construct a 2×2 matrix and obtain the Hill cipher for a message built using seven distinct letters of English alphabet. The total number of letters of the message may exceed seven. (10 points)

3. M44  is a set of 4 × 4 matrices, whose trace equals 12. Construct two distinct vector spaces, which are isomorphic to the given set. Verify that the constructed transformations are isomorphisms. (10 points)

4. Population growth in imaginary districts is described by the following table. Use the least- squares polynomial of degree 2 to predict populations for the year 2000.

Question for the Video Report

Present the solution for Question 4, record the video of your presentation in mp4 format and submit it in Microsoft Teams. (50 points)