Question 346674
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Do you just want the answer, or do you need the steps of procedure for some particular method of solving it?


I used Cramer's Rule.  Where the determinant of a 3X3 matrix is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ \left\[a_{11}\ a_{12}\ a_{13}\cr a_{21}\ a_{22}\ a_{23}\cr a_{31}\ a_{32}\ a_{33}\right\]\ \ \Rightarrow]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \det(A)\ =\ a_{11}a_{22}a_{33}\ +\ a_{12}a_{23}a_{31}\ +\ a_{13}a_{21}a_{32}\ -\ a_{31}a_{22}a_{13}\ -\ a_{32}a_{23}a_{11}\ -\ a_{33}a_{21}a_{12}] 


Using MS Excel to calculate the determinants, I got:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ D\ =\ -1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ D_x\ =\ 3]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ D_y\ =\ -6]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ D_z\ =\ 2]


Hence


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{D_x}{D}\ =\ \frac{3}{-1}\ =\ -3]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \frac{D_y}{D}\ =\ \frac{-6}{-1}\ =\ 6]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ z\ =\ \frac{D_z}{D}\ =\ \frac{2}{-1}\ =\ -2]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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