Homework 1 solution

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This homework contains 5 questions. The last question requires programming. The maximum number
of points is 100 plus 10 bonus points.
For Questions 3, 4, and 5 (and it is a good idea in general), we will use the following notations. Bold
uppercase letters denote matrices (e.g. D), bold lowercase letters denote column vectors (e.g. d). di
represents the i
th column of the matrix D. dij denotes the scalar in the row j
th and column i
th of the matrix
D; it is also the j
th entry of column vector di
. Non-bold letters represent scalar variables. 1k ∈