Consider the matrix multiplication C = AB. A matrix W is called a witness matrix with the following conditions: • If ci j = 0, then wi j = 0. • If ci j = 1, then wi j = k where aik = bkj = 1. make code to displays two Booelan matrices A and B and their product C. Note that we define these matrices with 0 and 1 entries and declare their types as boolean with dtype = bool statement after specifying the entries. Alternatively, we could have specified theses matrices with True and False entries. The boolean product C is then converted to integer by the astype method and both forms of C are printed

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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.