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frx

The vectors (1,2,3,4),(0,1,2,3),(0,0,1,2),(0,0,0,1) creates a basis in R^4. Decide the coordinates for the vector (1,1,1,1) in the given basis.

  • one year ago
  • one year ago

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  1. frx
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    The answer is (1,-1,0,0) however I don't know how to get there.

    • one year ago
  2. Tushara
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    • one year ago
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  3. Tushara
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    i hope that helps, all u need is a vectors that u can multiply the basis with to get [1 1 1 1]

    • one year ago
  4. Tushara
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    vector*

    • one year ago
  5. frx
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    Ohh I see, thank you very very much! :)

    • one year ago
  6. RolyPoly
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    Excuse me, why do we use row vectors instead of column vectors in this case? Are the two the same?

    • one year ago
  7. Tushara
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    actually, the basis is given to us, so we dont need to find it, but if we were to find it then we have to put the vectors in columns.... frx gave the basis as row vectors, the question was not in proper notation

    • one year ago
  8. RolyPoly
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    Does that mean when we do this question, we put the vectors in rows, since the given vectors are row vectors. When the given vectors are column vectors, when we need to put it in columns? I'm sorry, I'm quite confused.

    • one year ago
  9. RolyPoly
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    Also, how do you find the B for \(B \cdot A\)? And.... Why is the multiplication correct? I mean B is a 1x4 matrix and A is a 3x4 matrix. How can we find the matrix product \(B \cdot A\)?

    • one year ago
  10. Tushara
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    matrix multiplication works like that.... matrices dont need to be the same size to multiply dem

    • one year ago
  11. Tushara
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    check out example 1 here: http://www.mathwarehouse.com/algebra/matrix/multiply-matrix.php

    • one year ago
  12. RolyPoly
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    The problem is that for matrix multiplication, we need the number of columns of the first matrix equal to the number of rows of the second matrix. But in your working, B is a 1x4 matrix, while A is a 3x4 matrix. The number of columns of B is not equal to the number of rows of A, so, I think the matrix multiplication is undefined.

    • one year ago
  13. Tushara
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    A is a 4x4 matrix... take a look at it again, u didnt see it right

    • one year ago
  14. RolyPoly
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    I see the problem now... The first matrix A is a 4x4 matrix. But when you write BA, the matrix A there is of the size 3x4. You missed the third row there. I was looking at that BA, and didn't realise that you missed a row there. Sorry!!!

    • one year ago
  15. Tushara
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    ohhh yes, i did miss a row, sorry

    • one year ago
  16. RolyPoly
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    Thanks a lot though! I understand how to do this question now :)

    • one year ago
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