Linear Algebra

posted by .

Solve the following system using Gauss's algorithm

(a)
x1 + 2x2 + 4x3 + 6x4 = 3
2x1 + x2 + 3x3 = -6
-2x1 + x2 + 6x3 + 4x4 = -11
2x1 + x2 + x3 = 0

so the matrix will be:

1 2 4 6 3
2 1 3 0 -6
-2 1 6 4 -11
2 1 1 0 0

  • Linear Algebra -

    numbering the lines 1-4,

    #2 - 2*#1, #3 + 2*#1, #4 - 2*#1 gives

    1 2 4 6 3
    0 -3 -5 -12 -12
    0 5 14 16 -5
    0 -3 -7 -12 -6

    Follow similar steps to place zeros in the other rows off the main diagonal, to end up with

    so, (x1,x2,x3,x4) = 1/3 (-23,55,-9,-7)


    A good calculator which shows the steps can be found at

    www.gregthatcher.com/Mathematics/GaussJordan.aspx

  • Linear Algebra -

    awesome, thanks a lot Steve, that link will come in handy!

  • Linear Algebra -

    sure thing. Plus, I messed up my math. Solution is really (1,1,-3,2)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Linear Programming

    calculate the lower bound from min z= 4x1 + 2x2 2x1 - 3x2 => 4 x1 + 5x2 <= 6 2x1 - 6x2 = 10 x1=>0
  2. math,help

    this is from another section one of the problems can someone help me. dierections: use the simplex method to solve each linear programming problem. maximize z = 12x1 +15x2 +5x3 subject to: 2x1+2x2+x3 <= 8 x1+4x2+3x3<=12 with …
  3. Operations research

    36) Consider the following minimization problem: Min z = x1 + 2x2 s.t. x1 + x2 ≥ 300 2x1 + x2 ≥ 400 2x1 + 5x2 ≤ 750 x1, x2 ≥ 0 What is the optimal solution?
  4. maths

    Write the system as a matrix equation and solve using inverses. x1 + 2x2 - x3 = -3 -2x1 - x2 + 3x3 = 0 -4x1 + 4x2 - x3 = -12 A. x1 = 2, x2 = -3, x3 = 1 B. x1 = 1, x2 = -2, x3 = 1 C. x1 = 1, x2 = -2, x3 = 0 D. x1 = 1, x2 = -3, x3 = …
  5. linear algebra

    If possible, solve the following linear systems by Cramer's rule. 2x1 + 4x2 + 6x3 = 14 x1 + 2x3 = 0 2x1 + 3x2 − x3 = 30
  6. linear

    If possible, solve the following linear systems by Cramer's rule. 2x1 + 4x2 + 6x3 = 14 x1 + 2x3 = 0 2x1 + 3x2 − x3 = 30 i am having trouble with this one
  7. pesh uni

    2x1+2x2+2x3=0 -2x1+5x2+2x3=1 8x1+x2+4x3=1 gauss elimnation method plz sol any one
  8. M240 Help please

    Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination. a. 3x1 + 5x2 - 8x3 + 5x4 = -8 b. x1 + 2x2 - 3x3 + x4 = -7 c. 2x1 + 3x2 - 7x3 + 3x4 = -11 d. 4x1 + …
  9. math

    use simplex method solbe LPP maximize Z=2x1+4x2+x3+x4 subject to x1+3x2+x4<4 2x1+x2<3 x2+4x3+x4<3 x1,x2,x3,x4>0
  10. math

    use simplex method solbe LPP maximize Z=2x1+4x2+x3+x4 subject to x1+3x2+x4<4 2x1+x2<3 x2+4x3+x4<3 x1,x2,x3,x4>0

More Similar Questions