(a) Prove that any regular symmetric matrix can be decomposed as a linear combination
K = d1,11IT1 + d2I21T2 + €¢ €¢ €¢ + dn11lT1 (3.69)
of symmetric rank 1 matrices, as Exercise 1.8.15. where 11.......1n are the columns of the special lower triangular matrix L and d1,... , dn are the pivots, i.e., the diagonal entries of D. Hint: See Exercise 1.2.34.
(b) Decompose

this manner.

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