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lvl10720-Turquoise
20-Turquoise
October 12, 2022
Solved

Solve, Matrix [3x3] ?

Hi, Everyone.
From the following:

1.PNG

How to solve, the Matrix [3x3] ?


Thanks in advance for your time and help.
Best Regards.
Loi.

 

lvl107Answer
20-Turquoise
October 27, 2022

Just changing "solve, a, b, c" into "solve, b, c, a"

0.PNG 

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7 replies

Werner_E
Werner_E25-Diamond I
25-Diamond I
October 12, 2022

Your problem has a myriad of solutions!

Why not simply use the built-in symbolics?

Werner_E_0-1665602846279.png

With this approach the four solutions depend on Z.

Werner_E_1-1665603024820.png

But you may as well make the solution(s) dependent on, lets say, Y:

Werner_E_2-1665603162674.png

 

 

 

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    lvl10720-TurquoiseAuthor
    20-Turquoise
    October 12, 2022
    @Werner_E wrote:

    Why not simply use the built-in symbolics?

     

    Many thanks, Werner. I follow your suggestion then :

    2.PNG

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    Werner_E
    Werner_E25-Diamond I
    25-Diamond I
    October 12, 2022

    You got a set of seven solution triples.

    If there are more dependent on one (or even more) parameters, you may get them by using the modifier "fully" as you can see in my sheet and screenshot.

     

    It looks like Mathcad also delivers three "solutions" which simply are wrong!

    We don't see the symbolic solution because its too large to display, but we can assume it contains a parameter "-z" and assign the result to a function.

    The first four solutions are always the same and independent on _z, the last three solutions simply are wrong 😞

    Werner_E_0-1665609296398.png

    BTW, Prime6 with the new symbolic engine simply throws a "No solution was found."

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    LucMeekes23-Emerald IV
    23-Emerald IV
    October 12, 2022

    LucMeekes_0-1665610073993.png

    In case Z=(sqrt(5)-1)/4, you get:

    LucMeekes_1-1665610138326.png

    The solution you're after is on the 4th row, when you realise that:

    LucMeekes_2-1665610266039.png

    Success!
    Luc

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      lvl10720-TurquoiseAuthor
      20-Turquoise
      October 12, 2022

      Many thanks, Luc. I guess you using Mathcad 11. Try with second example and check it out there can eliminate Werner's last 3 solutions. And my Mathcad 15 then:

      3.PNG

      ( 5 minutes waiting but get no result. ) 

      Regards.

      Loi.

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      Werner_E
      Werner_E25-Diamond I
      25-Diamond I
      October 12, 2022

      You deleted the constraint "assume, ALL=real" and as it seems Mathcad has a hard time to do the necessary case distinctions as it also tries to consider the case that some or all parameters are non-real.

      As already written, Mathcad 15 and Prime with muPad delivers three additional wrong solutions additionally to the five correct ones.

      And the new symbolic in Prime is not able at all  to find a single solution.

      So I am curious, too, what Maple in MC11 can come up with 😉

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