hw1.pdf - Linear Algebra Fall 2018 HW#1 Please give complete well-written solutions to the following exercises Show all work to relieve full credit

hw1.pdf - Linear Algebra Fall 2018 HW#1 Please give...

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Linear Algebra - Fall 2018 HW #1 Please give complete, well-written solutions to the following exercises. Show all work to relieve full credit! Total number of points: 65 (1) (5 points) At the beginning of the first class we watched the movie ”Flatland”. Describe the idea of dimension and how to describe a point in a space of a certain dimension (based on what was shown/explained in the movie). Write about 5-10 lines. (2) (5 points) Draw a head-to-tail diagram in the same xy -plane to represent the vectors v = 4 1 , w = - 2 2 , v + w and v - w . (3) (5+5=10 points) Consider a clock with labeled hours 1:00, 2:00, . . . , 12:00. (a) Find sum of 12 vectors that go from the center of the clock to the hours 1:00, 2:00, . . . , 12:00. (b) Now suppose the 12 vectors start from 6:00 instead of the center and go to the hours 1:00, 2:00, . . . , 12:00. Find the sum. (4) (5+5=10 points) (a) Find the forward difference matrix A that acts on x = x 1 x 2 x 3 such that A x = b where b = b 1 b 2 b 3 = x 2 - x 1 x 3 - x 2 0 - x 3 .
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