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    Hello I'm just wondering if anyone could help with question 7 in the attachment it's mainly the first part that's causing me problems as I'm not too sure what matrices it's asking for with the notation used thanks again

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    (Original post by Scary)
    Hello I'm just wondering if anyone could help with question 7 in the attachment it's mainly the first part that's causing me problems as I'm not too sure what matrices it's asking for with the notation used thanks again
    Hi. I'm not at uni yet as I can see this is uni based, but I did FP4 for Further Maths. I haven't used Cramer's rule at A-Level a lot due to alternatives I preferred, and when I did it was with 3x3 matrices, so since these are 4 variables with 4 equations I assume that A, B_x and B_t will be 4x4 matrices each? I don't know how to find 4x4 determinants, though, so that's up to you.

    If that is the case, then:

    A=\begin{vmatrix} -3 & 2 & -1 & 1 \\4 & -8 & 7 & 3 \\-1 & -1 & -1 & -1 \\2 & 1 & -6 & 4 \end{vmatrix} (matrix of coefficients)

    B_x=\begin{vmatrix} -26 & 2 & -1 & 1 \\45 & -8 & 7 & 3 \\-2 & -1 & -1 & -1 \\-26 & 1 & -6 & 4 \end{vmatrix} (coefficients of x get replaced with constants)

    B_t=\begin{vmatrix} -3 & 2 & -1 & -26 \\4 & -8 & 7 & 45 \\-1 & -1 & -1 & -2 \\2 & 1 & -6 & -26 \end{vmatrix} (coefficients of t get replaced with constants)

    Then it follows that x=\frac{B_x}{A} and t=\frac{B_t}{A}

    Edit: It might also make it easier to multiply through by -1 on the third equation? Change the signs where applicable within the determinants if you choose to do so
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    thank you for your response i couldnt remember what the subscript was referring to within the question, and for finding the determinate of a 4x4 matrix you would just get it into rref so its upper triangle is the only part with non zeros and then you would multiple the diagonal(from left to right) to get the determinant
 
 
 
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