Solution Found!
Use Gaussian elimination to solve the following systems of linear equations. (a) (c) (d)
Chapter 3, Problem 2(choose chapter or problem)
Use Gaussian elimination to solve the following systems of linear equations. (a) (c) (d) (e) (g) (h) Xi + 2X2 X3 = 1 2xi + 2x2 + X3 = 1 (b) 3xi + 5x2 2.X3 1 xi + 2x2 + 2x4 = 6 3xi + 5x2 X3 + 6x4 = 17 2xi + 4x2 + x3 + 2x4 = 12 2xi 7x3 + HX4 = 7 x\ x2 2x3 + 3x4 = 7 2xi X2 + 6x3 + 6x4 = 2 2X] + X2 4X3 ~" 3X4 = 0 3xi 2x2 + 9^3 + IOX4 = 5 Xi - 2xi - 3xi - Xi - 2x2 - X3 - 3x2 +- x3 - 5x2 + 5x3 = 1 = 6 = 7 = 9 xi - 4x2 - x3 + x4 = 3 2xi - 8x2 + X3 4x4 = 9 -X! + 4x2 - 2x3 + 5x4 = -6 2xi 2x2 X3 + 6x4 2x5 = 1 .X'i X2 + X3 + 2x4 X5 = 2 4xi - 4x2 + 5x3 + 7x4 - x5 = 6 3xi X2 + X3 X4 + 2x5 = 5 X] - x2 - x3 - 2x4 - x5 = 2 5xi - 2x2 + x-s - 3x4 + 3x5 = 10 2xi X2 2x4 + X5 = 5
Questions & Answers
QUESTION:
Use Gaussian elimination to solve the following systems of linear equations. (a) (c) (d) (e) (g) (h) Xi + 2X2 X3 = 1 2xi + 2x2 + X3 = 1 (b) 3xi + 5x2 2.X3 1 xi + 2x2 + 2x4 = 6 3xi + 5x2 X3 + 6x4 = 17 2xi + 4x2 + x3 + 2x4 = 12 2xi 7x3 + HX4 = 7 x\ x2 2x3 + 3x4 = 7 2xi X2 + 6x3 + 6x4 = 2 2X] + X2 4X3 ~" 3X4 = 0 3xi 2x2 + 9^3 + IOX4 = 5 Xi - 2xi - 3xi - Xi - 2x2 - X3 - 3x2 +- x3 - 5x2 + 5x3 = 1 = 6 = 7 = 9 xi - 4x2 - x3 + x4 = 3 2xi - 8x2 + X3 4x4 = 9 -X! + 4x2 - 2x3 + 5x4 = -6 2xi 2x2 X3 + 6x4 2x5 = 1 .X'i X2 + X3 + 2x4 X5 = 2 4xi - 4x2 + 5x3 + 7x4 - x5 = 6 3xi X2 + X3 X4 + 2x5 = 5 X] - x2 - x3 - 2x4 - x5 = 2 5xi - 2x2 + x-s - 3x4 + 3x5 = 10 2xi X2 2x4 + X5 = 5
ANSWER:Step 1 of 10
(a)
Write the augmented matrix as:
Apply gauss elimination to the augmented matrix and solve as:
The corresponding last matrix gives the solution as:
