Question 311396
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left|\ 1\ \ \ 3\ \ \ 4\ \ \ 14\cr\ 2\ -3\ \ \ 2\ \ \ 10\cr\ 3\ -9\ \ \ 1\ \ \ \ 9\right|]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ R2\ -\ 2R1\ \rightarrow\ R2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left|\ 1\ \ \ 3\ \ \ 4\ \ \ 14\cr\ 0\ -9\ -6\ -18\cr\ 3\ -9\ \ \ 1\ \ \ \ 9\right|]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ R3\ -\ 3R1\ \rightarrow\ R3]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left|\ 1\ \ \ \ 3\ \ \ \ 4\ \ \ \ 14\cr\ 0\ \ -9\ \ -6\ -18\cr\ 0\ -18\ -11\ \ -33\right|]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{R3}{-9}\ \rightarrow\ R3]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left|\ 1\ \ \ \ 3\ \ \ \ 4\ \ \ \ 14\cr\ 0\ \ \ \ 1\ \ \ \ \frac{2}{3}\ \ \ \ \ 2\cr\ 0\ -18\ -11\ -33\right|]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ R3\ +\ 18R2\ \rightarrow\ R3]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left|\ 1\ \ \ \ 3\ \ \ \ 4\ \ \ 14\cr\ 0\ \ \ \ 1\ \ \ \ \frac{2}{3}\ \ \ \ 2\cr\ 0\ \ \ \ 0\ \ \ \ 1\ \ \ \ 3\right|]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ R2\ -\ \frac{2}{3}R3\ \rightarrow\ R2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left|\ 1\ \ \ \ 3\ \ \ \ 4\ \ \ 14\cr\ 0\ \ \ \ 1\ \ \ \ 0\ \ \ \ 0\cr\ 0\ \ \ \ 0\ \ \ \ 1\ \ \ \ 3\right|]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ R1\ -\ 3R2\ \rightarrow\ R1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left|\ 1\ \ \ \ 0\ \ \ \ 4\ \ \ 14\cr\ 0\ \ \ \ 1\ \ \ \ 0\ \ \ \ 0\cr\ 0\ \ \ \ 0\ \ \ \ 1\ \ \ \ 3\right|]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ R1\ -\ 4R3\ \rightarrow\ R1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left|\ 1\ \ \ \ 0\ \ \ \ 0\ \ \ \ 2\cr\ 0\ \ \ \ 1\ \ \ \ 0\ \ \ \ 0\cr\ 0\ \ \ \ 0\ \ \ \ 1\ \ \ \ 3\right|]


So: *[tex \LARGE x\ =\ 2], *[tex \LARGE y\ =\ 0], and *[tex \LARGE z\ =\ 3]


Check:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \,(2)\ +\ 3(0)\ +\ 4(3)\ =\ 2\ +\ 12\ =\ 14]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2(2)\ -\ 3(0)\ +\ 2(3)\ =\ 4\ +\ \ \,6\ =\ 10]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3(2)\ -\ 9(0)\ +\ \ \,(3)\ =\ 6\ +\ \ \,3\ =\ 9] 


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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