5. Consider the equations, X₁ + 2x2 − x3 = 1, 2x₁ - x2 + x3 = 3, −X₁ + 2x2 + 3x3 = 7. a) Write the system in the form (A

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5 Consider The Equations X 2x2 X3 1 2x X2 X3 3 X 2x2 3x3 7 A Write The System In The Form A 1 (261.37 KiB) Viewed 33 times

5. Consider the equations, X₁ + 2x2 − x3 = 1, 2x₁ - x2 + x3 = 3, −X₁ + 2x2 + 3x3 = 7. a) Write the system in the form (A|b) and solve for x = (x₁, x2, x3) by Gaussian elimination (i.e. reduction to upper triangular form and back substitution, no pivoting). What are the multipliers? What are the pivots? b) Find the LU factorization of A and check that LU A. Solve for x by forward and back substitution, i.e. Ly = b, Ux = y. The result should be the same as in part (a). = c) Compute the determinant of A two ways, first by the usual method and second by the formula det A (1) (2) (3) (k) a11 a22 a33, where akk is the pivot element in step k of Gaussian elimination. =