Question 392754
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Create the augmented matrix (after swapping equatons 1 and 2):


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left\[\ 1\ \ 5\ -1\ \ 4\cr\ 0\ \ 3\ -1\ -1\cr\ -3\ \ 6\ \ 2\ 11\right\]]


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


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left\[\ 1\ \ 5\ -1\ \ 4\cr\ 0\ \ 3\ -1\ -1\cr\ 0\ 21\ -1\ 23\right\]]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -7R2\ +\ R3\ \rightarrow\ R3]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left\[\ 1\ \ 5\ -1\ \ 4\cr\ 0\ \ 3\ -1\ -1\cr\ 0\ \ 0\ \ 6\ 30\right\]]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{R3}{6}\ \rightarrow\ R3]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left\[\ 1\ \ 5\ -1\ \ 4\cr\ 0\ \ 3\ -1\ -1\cr\ 0\ \ 0\ \ 1\ \ 5\right\]]


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


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left\[\ 1\ \ 5\ -1\ \ 4\cr\ 0\ \ 3\ \ 0\ \ 4\cr\ 0\ \ 0\ \ 1\ \ 5\right\]]


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


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left\[\ 1\ \ 5\ -1\ \ 4\cr\ 0\ \ 1\ \ 0\ \ \frac{4}{3}\cr\ 0\ \ 0\ \ 1\ \ 5\right\]]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ R3\ +\ R1\ \rightarrow\ R1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left\[\ 1\ \ 5\ \ 0\ \ 9\cr\ 0\ \ 1\ \ 0\ \ \frac{4}{3}\cr\ 0\ \ 0\ \ 1\ \ 5\right\]]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -5R2\ +\ R1\ \rightarrow\ R1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left\[\ 1\ \ 0\ \ 0\ \ \frac{7}{3}\cr\ 0\ \ 1\ \ 0\ \ \frac{4}{3}\cr\ 0\ \ 0\ \ 1\ \ 5\right\]]


One question per post.  Repost the other two -- IF you still need the help.


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