A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

Which values of constant k does the system of linear equations give exactly one solution (x1)+(4x)(2)=1 and (3)(x1) + (12)(x2) = k

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Is this the system you are trying to solve? $$x_1 + 4x_2 = 1$$ $$3x_1 + 12 x_2 = k$$

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Is it any number except 3?

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    because if its 3 then there will be infinite solutions

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    If so, the answer is that there is no such value. There is one value for which there is an infinite number of solutions, and an infinite number of values for which there are no solutions. To prove it, consider that two equations have a unique solution if and only if the determinant of the coefficient matrix is zero. But the determinant of the coefficient matrix in this case is \(12\times1 - 3\times 4 = 0\). Note that \(k\) plays no part in it, so no amount of tweaking \(k\) can change the determinant.

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    What do you mean by determinant of the coefficient matrix?

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The coefficients infront of each x?

  8. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes. The determinant of a matrix is a complicated beast, but for a 2x2 matrix is as below: $$ \det\begin{bmatrix} a & b \\ c & d \end{bmatrix} = ad - bc $$

  9. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    doesnt the answer of each equation go into the matrix as well?

  10. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    like for the equations shouldn't it be like 1 4 1 3 12 k

  11. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sorry I'm new to matrix

  12. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes, but the coefficient matrix is the one that is made up by just the coefficients of the variables. So, in this case, it's: $$\begin{bmatrix}1 & 4 \\ 3 & 12\end{bmatrix}$$

  13. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.