Q4. Prove that the LU factorization is unique by considering the possibility that LU = LŨ, for some L, L lower triangular matrices, U,Ũ upper triangular matrices, such that L+L or U # U. (Hint: you will need HW 2 Q3, and discussion week 2 Q3.) Note: For the LU decomposition, we always choose L such that it has only 1s on its diagonal. You should assume this property for L and L.

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Q: Factorize the matrix into LU decomposition. A=[ 054 512 123 Note; With complete solution

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Q: 8.7.1. Find the singular values of the following matrices: 1 -2 (c) › (_-²-²) -3 6

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A: Please see the below picture for detailed solution.

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Q: [: ] 4. Let A Show Ais the product o f elementary 2 4 matrices

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