1. Reduce the following matrix A to a diagonal form (A') by integer row and column operations and determine the integer matrix P-1 and Q such that A' = QAP-1 is a diagonal matrix. 3 1 A = -3 1 -4 -2)...

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Extracted text: 1. Reduce the following matrix A to a diagonal form (A') by integer row and column operations and determine the integer matrix P-1 and Q such that A' = QAP-1 is a diagonal matrix. 3 1 A = -3 1 -4 -2) 2. Find the basis for the submodule of Z3 which is the module of solutions of the system of equations: x + 2y + 3z = 0 x + 4y + 9z = 0. 3. For V = e, find the ring of endomorphisms of V. 6Z