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Implement basic matrix operations and matrix decompositions. 1. Basic matrix operations: +, -, .*, *, ', determinant, inverse, rank etc. 2. Matrix decompositions: LU decomposition, QR decomposition. Implement basic matrix operations and matrix decompositions. 1. Basic matrix operations: +, -, .*, *, ', determinant, inverse, rank etc. 2. Matrix decompositions: LU decomposition, QR decomposition. Implement basic matrix operations and matrix decompositions. 1. Basic matrix operations: +, -, .*, *, ', determinant, inverse, rank etc. 2. Matrix decompositions: LU decomposition, QR decomposition. Implement basic matrix operations and matrix decompositions. 1. Basic matrix operations: +, -, .*, *, ', determinant, inverse, rank etc. 2. Matrix decompositions: LU decomposition, QR decomposition.