6 7 0 1 2 3 - Find A X B A = B = 8 3 4 5 10 11 -2 4- Determining Whether a 3 x 3 Matrix A is Orthogonal or not. A = -1 -2 12 1

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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.