Linear Algebra

posted by .

Express the solutions of the following systems in terms of the free variables:

x1 + 3*(x2) - 2*(x3) + 2*(x5) = 0
2*(x1) + 6*(x2) - 5*(x3) - 2*(x4) + 4*(x5) - 3*(x6) = -1
5*(x3) + 10*(x4) + 15*(x6) = 5
2*(x1) + 6*(x2) + 8*(x4) + 4*(x5) + 18*(x6) = 6

  • Linear Algebra -

    Hey Linus,

    First step: simplify where you can. For example, equation 3 can be divided by 5, so you end up with (x3) + 2(x4) + 3(x6) = 1. Equation 4 can also be simplified. This will make the algebra later a little easier.

    Second step: Pick an x (x1 seems to be a good one) to start solving, and begin moving around your equations.

    Do you know where to go from here? (Or are you onto matrices already? If so ignore step 2 and build your matrix). If you're stuck show me what you've done so far and I'll help out!

  • Linear Algebra -

    I got:

    x1 = -3*(x2) -2*(x5) + 66*(x6) - 22
    x2 = free
    x3 = 33*(x6) - 11
    x4 = -18*(x6) + 6
    x5 = free
    x6 = free

    Is that correct?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    Solve the system by the method of your choice. Identify systems with no solutions and systems with infinitely many solutions, using set notation to express their solutions: (0 ,-5) (0 , 0) (-2 ,-1) (-2,-3)
  2. calculus

    Solve the system by the method of your choice. Identify systems with no solutions and systems with infinitely many solutions, using set notation to express their solutions: x + y = 3 -2 + y = -3 (0 ,-5) (0 , 0) (-2 ,-1) (-2,-3)
  3. algebra

    I do not know how to solve the following systems of linear equations in 3 variables 1) x-2y+z=7 2) 2x+y-3z=-1 3) x-4y+3z=13
  4. algebra

    systems of linear equations in 3 variables 1/3x-2/3y+z=0 1/2x-3/4y+z=1/4 -2x-y+z=1
  5. Algebra

    I have major issues with problems like these,please I need help. For these systems of linear equations in questions -Determine how many solutions exist -Use either elimination or substitution to find the solutions (if any) 1. y = 2x …
  6. Algebra

    Pulling my hair, need help! For the systems of linear equations in questions the following questions: Determine how many solutions exist Use either elimination or substitution to find the solutions (if any) 4x = 8 and 5y = 15 0.2x …
  7. Algebra 1

    How many solution sets do systems of linear inequalities have?
  8. Physics

    A point-like negatively charged particle of mass m and charge -q is initially released from rest from the point P along the positive z-axis where the magnitude of the electric field is largest. (a) What is the distance from the point …
  9. Physics

    Consider a capacitor made of two square plates of side l. The distance between the two plates is d . (a) We insert a dielectric of dielectric constant K>1 and width l a distance x (as in the diagram). What is the total capacitance …
  10. Algebra 1A

    How many solution sets do systems of linear inequalities have?

More Similar Questions