Question

1 (a) Employ the method of Gaussian elimination to solve the system of linear equations x+2y + 22= 4, 2x + y- z=-1 (b) State Cramer's rule for the solution of systems of linear equations, and use it to calculate the solution of the system of equations in (a)

Answer 1

x + 2y + 2z = 4 6x + 3y - 4z = 0 2x + y - 2 = 1 in matrix form [1 6 2 2 3 -1 2 - 4 - 1: : : 4 0 1] apply row transformation to reduce into row -echlon form R_2 rightarrow R_2 - 6R_1 R_3 rightarrow R_3 - 2R_1 [1 0 0 2 - 9 - 3 2 - 16 - 5: : : 4 - 24 - 7] R_2 rightarrow [1 0 0 2 1 - 3 2 16/g - 5: : : 4 8/3 - 7] R_1 rightarrow R_1 - 2R_2 [1 0 0 0 1 0 - 14/9 16/9 1/3: : : - 4/3 8/3 1] R_3 rightarrow R_3/3 [1 0 0 0 1 0 - 14/9 16/9 1: : : - 4/3 8/3 3] \r\n R_1 rightarrow R_1 + 14/9 R_3 R_2 rightarrow R_2 - 16/9 R_3 [1 0 0 0 1 0 0 0 1: : : 10/3 - 8/3 3] therefore x_1 = 10/3: y = -8/3 z = 3 b)
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