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    I know I've been completely stupid, left almost all my revision until the night before.

    I do NOT understand determinants, and the textbook is awful.

    Please can someone give me a quick explanation?
    • PS Reviewer
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    FP4??

    And determinants of a 2 by 2 matrix??

    If so, for a matrix \begin{vmatrix} a & b \\ c & d \end{vmatrix} the determinant is ad-bc

    If 3 by 3,

    then for a \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ a & b & c \\ d & e & f \end{vmatrix}

    we do \mathbf{i} \begin{vmatrix} b & c \\ e & f \end{vmatrix} - \mathbf{j} \begin{vmatrix} a & c \\ d & f \end{vmatrix} + \mathbf{k} \begin{vmatrix} a & b \\ d & e \end{vmatrix}
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    if you have the following matrix:

    [ A B C ]
    [ D E F ]
    [ G H I ]

    the determinant is A[EI - FH] - B[EI - FG] + C[DH - EG].

    if you're running out of time, just remember that algorithm (or write i down somewhere ).
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    I think for the sake of A-level maths there isn't much to explain. The only thing I can think of is knowing that a matrix is singular (i.e. Has no inverse) if and only if it has determinant zero. Do you learn the minors/cofactors method at A-level to work out an inverse of a 3x3 matrix? If so that's another reason to know about determinants.

    Just learn the formulae. The 2x2 case is just ad-bc; the 3x3 case just needs you to remember the method, which in all fairness is hardly difficult.

    I seem to remember quite a few questions coming up where you'd be given a matrix, say

    [ a 1 7 ]
    [ 3 2a 9]
    [16 6a 2]

    and having to work out the possible values of a given that the determinant is 42.

    Why not just go through past papers and pick out all the determinant questions? Papers should be readily available n the exam board website, especially if you're on AQA.
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    I was sure it only went up to FP3 :lolwut:
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    AQA I think goes to FP4
    • PS Helper
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    (Original post by J-E-N-O-V-A)
    I was sure it only went up to FP3 :lolwut:
    AQA has an FP4.
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    Several methods... The best for a 3x3 is expansion by first row or the diagnol lines thing (can't recall the name). Anything bigger than 3x3 and you may want to use dodgsons condensation method.
    • PS Helper
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    My method for 3x3 matrices works a treat. Say you have the matrix \displaystyle\begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i\end{pmatrix}, the determinant can be found by first summing the products of the diagonals from top-left to bottom-right; then subtracting the products of the diagonals from top-right to bottom-left. That is, aei + bfg + cdh - ceg - afh - bdi. It's great fun... it's really just an expansion of \displaystyle a\begin{vmatrix}e&f\\h&i\end{vma  trix} - b\begin{vmatrix}d&f\\g&i\end{vma  trix} + c\begin{vmatrix}d&e\\g&h\end{vma  trix}
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    Thank-you all, I think I just about understand it now. Wish me luck for tomorrow!
 
 
 
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