Question

Solve the system of equations using matrices. Use the Gaussian elimination method with back-substitution 3x + 3y + 6z = 12 3x + 2y + 2z = 7 2x + 4y + 192 = 11 The solution set is {000) (Simplify your answers.) ha ancier hovee

Answer 1

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on the augmented I Let us apply roussian elemination the given systim. morniala) of 3 6 12 6 3 12 R3 Ry As 3 2 7 o w w 7 2 2 2 2 A 8/3 573 11913 3 3 6 12 6 3 12 3 R₂-R, -5 -4 -5 |R2 + Rzy 872 573 93 0 0 0 7 3 3 6 12 4 R3 0 -4 A' O O 1 NOW A implies, 34 + 3y + 62 = 12 2 -y-42 = -5 2 = -1 Now, 8 and ② implies, => y = 1 implies, =145 y + 4 = -5 NOW, 0, and 3x + 27 -6 =12 => 36 =12-27 +6 => 3x = -9 => x=-3

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So the solution set is {-3, 9, -1}