2a1 - a2 + 3a3 = 4 -4a1 + 3a2 + 2a3 = 1 3a1 + a2 - a3 = 3 Above shows a given system of linear equations. i.Utilize the Gaussian elimination method to determine  the solution vector a1, a2 and a3. i.Utilize the LU decomposition by hand computations to get the upper & lower triangular matrices for the system above.Carefully list the steps to solve completely for the unknown values of a1, a2 & a3. N.b Utilize the elementary row operations for performing the calculation  & arrive at the final solution.

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A: Given :-  Let a linear system of equations Ax =b where A = 42-222-3-2-314    ,      b = 10,5,4T To…

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A: Topic:- matrix

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