Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

brinethery Group Title

Given that T is a linear transformation, derive a formula for T.

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. brinethery Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    • 2 years ago
    1 Attachment
  2. brinethery Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Joe, if you have to go, I will understand :-).

    • 2 years ago
  3. imranmeah91 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    bookmark

    • 2 years ago
  4. joemath314159 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    I need to think about this a little lol. I can see a way to solve the problem, but there might be a shorter way.

    • 2 years ago
  5. brinethery Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I just don't get how to solve these ridiculously hard questions. I would rather be doing diffEq than this!

    • 2 years ago
  6. joemath314159 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    First, do you notice that the vectors (1,0,1), (1,1,0), and (0,1,1) are linearly independent and form a basis?

    • 2 years ago
  7. brinethery Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes.

    • 2 years ago
  8. joemath314159 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Good, thats whats going to make this easy. Im going to type out the idea and post it, one sec.

    • 2 years ago
  9. joemath314159 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    • 2 years ago
    1 Attachment
  10. joemath314159 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    oops oops oops, i was typing too fast. I dont mean the columns of A are linear independent, i meant the columns of that matrix next to A.

    • 2 years ago
  11. brinethery Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh my gosh, why did I not think of that?! I should've known to invert that sucker!

    • 2 years ago
  12. joemath314159 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Here is the correction.

    • 2 years ago
    1 Attachment
  13. brinethery Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    You're a much better explainer than the book is!

    • 2 years ago
  14. joemath314159 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    i have to run. Im sure there is probably a shorter or more interesting solution. anyways, have a good day :)

    • 2 years ago
  15. brinethery Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Thanks you SO much, I really mean it.

    • 2 years ago
  16. imranmeah91 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I passed linear algebra because of joe

    • 2 years ago
  17. brinethery Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Joe is the man!

    • 2 years ago
  18. anonymoustwo44 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok so since we have a linear transformation, we then have an induced matrix A such that T(x)=Ax now since our output is an 2x1 matrix and that the vector x we input is an 3x1 matrix, then our induced matrix A is just a 2x3 matrix cause multiplying a 2x3 matrix with a 3x1 matrix will give us an output of 2x1 matrix. So if we find this matrix A, we could now find a formula :D. ok so let our matrix A be: \[A=\left[\begin{matrix}a & b & c\\ d & e & f\end{matrix}\right]\] now we'll get:

    • 2 years ago
  19. anonymoustwo44 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    • 2 years ago
    1 Attachment
  20. anonymoustwo44 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I just wrote the solution :)) its hard to type lots of matrices

    • 2 years ago
  21. brinethery Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Thank you very much for your solution. But might I ask why you didn't want to just take the inverse since the 3 vectors form a basis?

    • 2 years ago
  22. anonymoustwo44 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    because I won't get the induced matrix or any formula for T from that :D which means I won't get any answer from that

    • 2 years ago
  23. anonymoustwo44 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    anyways goodluck with linear algebra which is used in differential equations also and has lots of implications on engineering, physics, economics, biology, chemistry, and math itself.

    • 2 years ago
  24. brinethery Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I did the inverse on both sides and came up with the same answer as what you got. I think it's easy to find the formula if one of the matrices is square. If one of them is not square, then we use the longer method, which is doing an induced matrix and solving for a-f. Thank you for showing me the other way so that I can use this method for non-square matrices.

    • 2 years ago
  25. anonymoustwo44 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    oh okay :D

    • 2 years ago
    • Attachments:

See more questions >>>

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.