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brinethery

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

  • one year ago
  • one year ago

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  1. brinethery
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    • one year ago
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  2. brinethery
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    Joe, if you have to go, I will understand :-).

    • one year ago
  3. imranmeah91
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    bookmark

    • one year ago
  4. joemath314159
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    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.

    • one year ago
  5. brinethery
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    I just don't get how to solve these ridiculously hard questions. I would rather be doing diffEq than this!

    • one year ago
  6. joemath314159
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    First, do you notice that the vectors (1,0,1), (1,1,0), and (0,1,1) are linearly independent and form a basis?

    • one year ago
  7. brinethery
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    Yes.

    • one year ago
  8. joemath314159
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    Good, thats whats going to make this easy. Im going to type out the idea and post it, one sec.

    • one year ago
  9. joemath314159
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  10. joemath314159
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    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.

    • one year ago
  11. brinethery
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    Oh my gosh, why did I not think of that?! I should've known to invert that sucker!

    • one year ago
  12. joemath314159
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    Here is the correction.

    • one year ago
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  13. brinethery
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    You're a much better explainer than the book is!

    • one year ago
  14. joemath314159
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    i have to run. Im sure there is probably a shorter or more interesting solution. anyways, have a good day :)

    • one year ago
  15. brinethery
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    Thanks you SO much, I really mean it.

    • one year ago
  16. imranmeah91
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    I passed linear algebra because of joe

    • one year ago
  17. brinethery
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    Joe is the man!

    • one year ago
  18. anonymoustwo44
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    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:

    • one year ago
  19. anonymoustwo44
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  20. anonymoustwo44
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    I just wrote the solution :)) its hard to type lots of matrices

    • one year ago
  21. brinethery
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    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?

    • one year ago
  22. anonymoustwo44
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    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

    • one year ago
  23. anonymoustwo44
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    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.

    • one year ago
  24. brinethery
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    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.

    • one year ago
  25. anonymoustwo44
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    oh okay :D

    • one year ago
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