5 30 points 10 of which are bonus An n x n matrix A is called symmetric if A AT A symmetric matrix A is called positive definite

Question

5 30 points 10 of which are bonus An n x n matrix A is called symmetric if A AT A symmetric matrix A is called positive definite if x Ar 0 for all non zero n x 1 matrices z Now let A be such a symmetric positive definite matrix Let e be the i th column of the n x n identity matrix 5 1 In terms of e1 e2 en ef e e and A using the idea of matrix multiplication fill in the following blanks The i th row of A can be expressed as The i th column of A can be expressed as The entry at i th column and j th row of A can be expressed as 5 2 Let r a11 a12 ain be the first row of A Please determine the value of bi in terms of a11 ain such that the following matrix equation is true a11 012 T1 ain b 1 b12 1 1 b1 n 1 1 0 0 0 B where B is a n x n 1 matrix and all the entries of B that are not written are 0

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