Question

DETAILS LARLINALG8 1.R.033. ASK YOUR TEACHER Solve the system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, express x, y, and zin terms of the parameter t.) 2x + 3y + 32 3 6x + 6y + 127 = 13 12x + Oy -

Answer 1

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is : Given system 2x + 3y 3 z = 3 6x + - 13 tby + 122 12x tay = 2 Augmented matrix for Gaussian elimination is: 2 3 3 3 6 6 12 13 12 9 2 R₂ R₂-3R, R3 R₃-6R, 2 3 wo wo o ł w -3 - 9 -19 16 R₃₃-R₂ +3R ₂ 2 3 33 3 4 - 3 0 O 28 128 wo w 2 o w w lot 3 3 3 O - 3 3 4 O R - - Rath 2 3 3 3 -Y3 - O

-.. R + R, -3R-3Rg O 2 -V3 0 R, ef R, 72 -V3 So by to the system Gauss - Jordam elimination, 2= yz, y = -93 , 2 =) is the solution (2,3,3) % , -73,1) Thus