Question

Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists.

x + y + z = 9
2x - 3y + 4z = 7
x - 4y + 3z = -2

Answer 1

form the coefficient matrix and row reduce to echelon form

Answer 2

the last column will produce the solution

Answer 3

ok let me try thanks

Answer 4

if i didnt hit a wrong key .... looks like a row of zeros on the bottom for "infinite" solutions

Answer 5

lets test the determinant


-(-3-16+6)
1 1 1 1 1
2 -3 4 2 -3
1 -4 3 1 -4
+(-9+4-8)


(-9+4-8) - (-3-16+6)

(-17+4) - (-3-10)

(-13) - (-13)

-13 + 13 = 0

Answer 6

here is what i came up with 7z/5+ 34/5+2z/5+ 11/5z) looks like were off

Answer 7

I think it might be negitive im confused

Answer 8

1x + 1y + 1z = 9
2x - 3y + 4z = 7
1x - 4y + 3z = -2

\[\begin{pmatrix}1&1&1\\2&-3&4\\1&-4&3\\\end{pmatrix}~\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}9\\7\\-2\end{pmatrix}\]

\[\begin{pmatrix}1&1&1&|&9\\2&-3&4&|&7\\1&-4&3&|&-2\end{pmatrix}\to\begin{pmatrix}1&0&1.4&|&6.8\\0&1&-.4&|&2.2\\0&0&0&|&0\end{pmatrix}\]

\[x=6.8-1.4z\]
\[x=2.2+0.4z\]
\[z=~0~+1.0z\]

Answer 9

that was my ti83, the wolf does this

rref{{1,1,1,9},{2,-3,4,7},{1,-4,3,-2}}

http://www.wolframalpha.com/input/?i=rref%7B%7B1%2C1%2C1%2C9%7D%2C%7B2%2C-3%2C4%2C7%7D%2C%7B1%2C-4%2C3%2C-2%7D%7D

Answer 10

either way, we get an under row of all zeros, which tells me that 0 is always equal to 0, so infinite solutions

Answer 11

thank you very much!!

Answer 12

good luck :)