Prove that fill-in is restricted to the spikes of a

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Question: 1. The statement that "in computing the triangular factorization LnLn-1,..........,L1A = U fill-in occurs in the jth column" means that Lj has a nonzero entry lij where aij = 0 or U has a nonzero entry uij where aij = O. Prove that fill-in is restricted to the spikes of A.

2. Prove that the product of two lower triangular matrices is lower triangular and that the inverse of a nonsingular lower triangular matrix is lower triangular.

Reference no: EM131504731

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