2) Let a linear code have the following parity check matrix. [0 1 1 1 1 0 0] H = |1 0 1 1 0 1 0 li 1 0 1 0 0 1] a) Find its generator matrix G. b) List all the codewords by using the generator matrix found in (a).

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LUP Decomposition

LU decomposition stands for Lower-Upper decomposition. LU decomposition is the factorization of the lower triangular matrix and an upper triangular matrix. It is very useful in linear algebra and numerical analysis. A permutation matrix is usually included in the product. Gaussian elimination in a matrix form is known as LU decomposition, When inverting a matrix or evaluating its determinant, this is a crucial step. Tadeusz Banachiewicz, a Polish mathematician, first proposed the LU decomposition in 1938.