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    y_0 ^1 \cdot y_1 ^2 - y_0 ^2 \cdot y_1 ^1 \neq 0

    Then we have a fundamental set of solutions. Obviously we don't have a fundamental set if the values equal 0 but is there anything else i can say about the values or the equation they come from if the above is equal to 0?

    Like repeated roots or something?

    also do the subscript 0 and 1 mean to those powers?

    Edit:With the subscript of y^1\ and y^2 being 0 and 1 are the powers of the terms y^1\ and y^2 also to the powers of 0 or 1 for example is the termy_0 ^1 to the power of 0 when we sub in y^1 into y_0 ^1. Or do i have the wrong idea and misunderstood what the terms mean?


    And what does

    y_0 ^1 \cdot y_1 ^2 - y_0 ^2 \cdot y_1 ^1 \neq 0
    mean if the equality is actually equal to 0, is there anything else i should about this other than the fact that this does not form a fundamental set of solutions?


    Edit2: In the section of math models.

    Where a difference equation has a fundamental set if
    y_0 ^1 \cdot y_1 ^2 - y_0 ^2 \cdot y_1 ^1 \neq 0

    Where a fundamental set is a set of solutions which make up the general solution for example a_n =A(5)^n +B(2)^n where 5 and 2 are part of a fundamental set only if they satisfy the formula(i think)

    If you stick 5 and 2 into this y_0 ^1 \cdot y_1 ^2 - y_0 ^2 \cdot y_1 ^1 \neq 0 do you get (5)^0 x (2)^1 - (2)^0 x (5)^1 or do you not use 0 and 1
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    What?
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    (Original post by math42)
    What?
    now read again, it's edited
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    (Original post by will'o'wisp2)
    now read again, it's edited
    I would like to repeat the earlier "what?" Put some detail and context into your question, otherwise people won't be able to help you.
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    (Original post by RichE)
    I would like to repeat the earlier "what?" Put some detail and context into your question, otherwise people won't be able to help you.
    ok sure check again
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    (Original post by will'o'wisp2)
    ok sure check again
    You really are not clarifying anything there. If you don't know whether the superscripts denote powers then you have to give us some context regarding what the variables mean. The only thing I might meaningfully offer is that it looks like a 2x2 determinant being nonzero - but that's just some educated guess.

    Why are 0 and 1 used for subscripts?
    Why are 1 and 2 used for superscripts?
    What do these variables denote and where did the question come from?
    What is a fundamental set? (I googled this and found nothing helpful)
    Also what does the dot mean - is that multiplication or perhaps the scalar product?
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    (Original post by will'o'wisp2)
    y_0 ^1 \cdot y_1 ^2 - y_0 ^2 \cdot y_1 ^1 \neq 0

    Then we have a fundamental set of solutions. Obviously we don't have a fundamental set if the values equal 0 but is there anything else i can say about the values or the equation they come from if the above is equal to 0?

    Like repeated roots or something?

    also do the subscript 0 and 1 mean to those powers?

    Edit:With the subscript of y^1\ and y^2 being 0 and 1 are the powers of the terms y^1\ and y^2 also to the powers of 0 or 1 for example is the termy_0 ^1 to the power of 0 when we sub in y^1 into y_0 ^1. Or do i have the wrong idea and misunderstood what the terms mean?


    And what does

    y_0 ^1 \cdot y_1 ^2 - y_0 ^2 \cdot y_1 ^1 \neq 0
    mean if the equality is actually equal to 0, is there anything else i should about this other than the fact that this does not form a fundamental set of solutions?
    is this something to do with DEs? As RichE said it looks like a det so maybe a wronskian? though what the exponents quite mean I'm unsure.
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    (Original post by RichE)
    You really are not clarifying anything there. If you don't know whether the superscripts denote powers then you have to give us some context regarding what the variables mean. The only thing I might meaningfully offer is that it looks like a 2x2 determinant being nonzero - but that's just some educated guess.

    Why are 0 and 1 used for subscripts?
    Why are 1 and 2 used for superscripts?
    What do these variables denote and where did the question come from?
    What is a fundamental set? (I googled this and found nothing helpful)
    Also what does the dot mean - is that multiplication or perhaps the scalar product?
    ok i see

    ah right ok more context got it check again
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    (Original post by _gcx)
    is this something to do with DEs? As RichE said it looks like a det so maybe a wronskian? though what the exponents quite mean I'm unsure.
    yup just edited again
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    (Original post by will'o'wisp2)
    Edit2: In the section of math models.

    Where a difference equation has a fundamental set if
    y_0 ^1 \cdot y_1 ^2 - y_0 ^2 \cdot y_1 ^1 \neq 0

    Where a fundamental set is a set of solutions which make up the general solution for example a_n =A(5)^n +B(2)^n where 5 and 2 are part of a fundamental set only if they satisfy the formula(i think)

    If you stick 5 and 2 into this y_0 ^1 \cdot y_1 ^2 - y_0 ^2 \cdot y_1 ^1 \neq 0 do you get (5)^0 x (2)^1 - (2)^0 x (5)^1 or do you not use 0 and 1
    I'm sorry but this really isn't helping much. We don't have the same set of lecture notes in front of us as you do to make sense of this.

    "In the section of math models." - that's rather vague/opaque and not helpful.

    "Where a fundamental set is a set of solutions which make up the general solution for example a_n =A(5)^n +B(2)^n where 5 and 2 are part of a fundamental set only if they satisfy the formula(i think)" - that very much doesn't say what a fundamental set is. Can you clarify? I do know how to solve linear difference equations (and wrote a chapter of a book on this recently) but still can't make sense of this.

    "If you stick 5 and 2 into this y_0 ^1 \cdot y_1 ^2 - y_0 ^2 \cdot  y_1 ^1 \neq 0 do you get (5)^0 x (2)^1 - (2)^0 x (5)^1 or do you not use 0 and 1" - how can we answer this, not knowing what anything means?

    I don't mean to be rude, but I have been on TSR for 12 years, frequently replying in the maths forum, and have never been so stumped/confused by a request for help.
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    (Original post by RichE)
    I'm sorry but this really isn't helping much. We don't have the same set of lecture notes in front of us as you do to make sense of this.

    "In the section of math models." - that's rather vague/opaque and not helpful.

    "Where a fundamental set is a set of solutions which make up the general solution for example a_n =A(5)^n +B(2)^n where 5 and 2 are part of a fundamental set only if they satisfy the formula(i think)" - that very much doesn't say what a fundamental set is. Can you clarify? I do know how to some linear difference equations (and wrote a chapter of a book on this recently) but still can't make sense of this.

    "If you stick 5 and 2 into this y_0 ^1 \cdot y_1 ^2 - y_0 ^2 \cdot  y_1 ^1 \neq 0 do you get (5)^0 x (2)^1 - (2)^0 x (5)^1 or do you not use 0 and 1" - how can we answer this, not knowing what anything means?

    I don't mean to be rude, but I have been on TSR for 12 years, frequently replying in the maths forum, and have never been so stumped/confused by a request for help.
    ok
    https://cdn.discordapp.com/attachmen...17/unknown.png
    https://cdn.discordapp.com/attachmen...64/unknown.png
    https://cdn.discordapp.com/attachmen...34/unknown.png
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    Thanks - so the superscripts refer to choices of independent solutions ot the recurrence relation and not to powers.

    The "preferred solutions" (1) and (2) are sequences of numbers and the subscripts then refer to the different terms of that sequence.
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    Let me further give an example which might clear things up.

    Consider the solutions - each of which will be a sequence - to the recurrence relation

    y_{n+2} = y_{n+1} + y_{n}

    where n is a non-negative integer

    One set of solutions are the Fibonacci numbers 0, 1, 1, 2, 3, 5, 8, 13, ...

    An independent set of solutions is 1, 1, 2, 3, 5, 8, 13, ....

    You might call the first y^1 and the second y^2.

    Subscripts would be referring to terms in these two sequences.

    And any sequence solving the recurence relations would be some linear combination of the two.
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    (Original post by RichE)
    Thanks - so the superscripts refer to choices of independent solutions ot the recurrence relation and not to powers.

    The "preferred solutions" (1) and (2) are sequences of numbers and the subscripts then refer to the different terms of that sequence.
    (Original post by RichE)
    Let me further give an example which might clear things up.

    Consider the solutions - each of which will be a sequence - to the recurrence relation

    y_{n+2} = y_{n+1} + y_{n}

    where n is a non-negative integer

    One set of solutions are the Fibonacci numbers 0, 1, 1, 2, 3, 5, 8, 13, ...

    An independent set of solutions is 1, 1, 2, 3, 5, 8, 13, ....

    You might call the first y^1 and the second y^2.

    Subscripts would be referring to terms in these two sequences.

    And any sequence solving the recurence relations would be some linear combination of the two.
    Right ok so we're talking the the 0th term of the 1st sequence, multiplied by the 1st term of the 2nd sequence minus the 0th term of the 2nd sequence multiplied by the 1st term of the first sequence, and as long as that isn't 0 we have a set of fundamental solutions?
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    (Original post by will'o'wisp2)
    Right ok so we're talking the the 0th term of the 1st sequence, multiplied by the 1st term of the 2nd sequence minus the 0th term of the 2nd sequence multiplied by the 1st term of the first sequence, and as long as that isn't 0 we have a set of fundamental solutions?
    Yes - that's a condition for the linear independence of the two sequences.
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    (Original post by RichE)
    Yes - that's a condition for the linear independence of the two sequences.
    ok thanks man
 
 
 
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