In Exercise 17–36, use the Gauss-Jordan elimination method to find all solutions of the system of linear equations.
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Finite Mathematics & Its Applications (12th Edition)
- In Exercises 7–10, determine the values of the parameter s for which the system has a unique solution, and describe the solution.arrow_forward6. Use Cramer’s Rule to solve for x3 of the linear system 2x1 + x2 + x3 = 63x1 + 2x2 − 2x3 = −2x1 + x2 + 2x3 = −4arrow_forwardExamine the system of linear equations in the form of λarrow_forward
- In Exercises 7–10, the augmented matrix of a linear system has been reduced by row operations to the form shown. In each case, continue the appropriate row operations and describe the solution set of the original system. 1 7 3 -4 1 -4 1 -1 3 7. 8. 1 7 1 1 -2 0 -4 0 -7 1 -1 1 -3 9. 1 -3 -1 4arrow_forward4) Use Cramer's rule to solve the following linear system: Iị – 3x2 + x3 = 4 2x1 – x2 = -2 4.x1 – 3.x3 = 0.arrow_forwardSolve the following linear equations using the 5 methods: (Gaussian Elimination, Gauss-Jordan Elimination, LU Factorization, Inverse Matrix and Cramer's Rule). Show your complete solutions. b. 2x1 — 6х, — Хз 3D — 38 -3x1 – x2 + 7x3 = -34 -8x1 + x2 – 2x3 = -20arrow_forward
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- 5. By using the matrix methods to solve the following linear system: I1 + 12 – 13 = 5, 3r1 +x2 – 2r3 = -4, -I1 + 12 - 2r3 = 3;arrow_forwardIn Exercises 13–17, determine conditions on the bi ’s, if any, in order to guarantee that the linear system is consistent. 13. x1 +3x2 =b1 −2x1 + x2 =b2 15. x1 −2x2 +5x3 =b1 4x1 −5x2 +8x3 =b2 −3x1 +3x2 −3x3 =b3 14. 6x1 −4x2 =b1 3x1 −2x2 =b2 16. x1 −2x2 − x3 =b1 −4x1 +5x2 +2x3 =b2 −4x1 +7x2 +4x3 =b3 17. x1 − x2 +3x3 +2x4 =b1 −2x1 + x2 + 5x3 + x4 = b2 −3x1 +2x2 +2x3 − x4 =b3 4x1 −3x2 + x3 +3x4 =b4arrow_forwardSolve the following linear system of equations using Gaussian Elimination methodarrow_forward
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