Solving equations using 3x3 determinants
Im trying to solve the following equations by use of determinants.
I have scanned my work sheet (sorry for the mess) but i cant see where i am going wrong. The equations are at the top, following by my working.
I am convinced that there is a silly mistake present in my working somwhere. So far i think that as i take the minor of the matrix, i should apply the alternating +,-,+,- etc to the leading term of the minor only (see work sheet).
therefore, terms within the small minor 2x2 matrix should be the true values as stated in the equations? Or should they follow the alternating +,-,+,- wiht obvious consideration given to the sign and how it affects the orginal sign of the term?
For the constant terms i have applyed the following method to arrive at the first value of -112
Following on from this, the X values are omitted and the value for delta X is found to be -280 as follows
Next, i found the deltaZ value to be -112 as follows
Using the same technique throughtout i found delta Y to be 336.
From all the delta values found, i then solved for X, Y and Z simply as follows
Y = 3
Although i checked the technique applied and the resultant values, the equations do not hold true so i am at a loss to the actual values of X, Y and Z
Thanks for any advice given
$\endgroup$ 41 Answer
$\begingroup$You did the same calculation for $\Delta_3$ as for $\Delta_0$. Instead, you need to replace the $z$ column by the right-hand column, like you did for $x$ to get $\Delta_1$.
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