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Q 1 Answer the following questions with justifications. a ) Given two linearly independent D 1 vectors v 1 and v 2 , where D
Q Answer the following questions with justifications.
a Given two linearly independent vectors and where we intend to create a matrix where each column of the matrix is a linear combination of the given vectors and If possible, find vectors and and values for the coefficients in the linear combination such that the resulting matrix has full column rank. Otherwise, explain with a suitable mathematical argument why this is not possible.
b Consider a matrix A which we can write as where is a lowertriangular matrix. We have a function that returns the value where is an matrix and and are vectors respectively. If we are given both the matrix A and what is the smallest number of calls that need to be made to this function in terms of in order to decide that the given matrix is positive definite, and why?
c We are given a function Can the series be the Taylor's polynomial to second degree that approximates this function around
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