3. Using the difference equation given below, Compute the theoretical results of the first 10 samples of y(n) using direct substitution and compare it to the result of the filter () function. y(n) = 0.7632y(n-1)-2.0173y(n-2) + 0.9964y(n-3) -1.4046y(n-4) + 0.3508y(n-5)-0.3144y(n-6) + 0.5610x(n) −0.5265x(n-1) + 1.8072x(n-2) - 1.0574x(n-3) + 1.8072x(n-4)-0.5265x(n-5) + 0.5610x(n-6). Zero initial conditions, x(n) = 5u(n) Obtain also the first 10 samples of h(n) and use this to solve again y(n) by convolving h(n) to x(n). Comment on the samples computed.

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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.