# Matrix ?

solve eqautions using a matrix

x + y -z = 0
3x - y + z = 4
5x +z = 7

so i wrote the matrix

1 1 -1 0
3 -1 1 4
5 0 1 7

then i multiplied Row 1 by -3 and added that to row 2
and multiplied row 1 by -5 and added that to row 3
resulting in

1 1 -1 0
0 -4 4 4
0 -5 6 7

then i multiplied row 2 by - 1/4

1 1 -1 0
0 1 -1 -1
0 -5 6 7

then multiplied row 2 by 5 and added that to row 3

1 1 -1 0
0 1 -1 -1
0 0 1 2

now i subbed back in to eqns

x + y -z = 0
3x - y + z = 4
5x +z = 7

1x + 1y - 1z = 0
0x +1y - 1z = -1
0x + 0y + 1z = 2

so z = 2 and solving all the other equation i get x = 1 and y = 1
is this right because i tried solving these by subtraction and got somthing different

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neu
You have not constructed a matrix equation, you have just rewritten the coefficients in some kind of array/pattern

THe matrix equation is :

$$\begin{pmatrix} 1 & 1 & -1\\ 3&-1 & 1\\ 5&0&1 \end{pmatrix} \begin{pmatrix} x\\ y\\ z \end{pmatrix} = \begin{pmatrix} 0\\ 4\\ 7 \end{pmatrix}$$

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The augmented matrix that 2slow to go fast used is correct.
All you need to do is plug x y and z back into your original equations and see if they make true statements.
Looks to me like they check out.
CC

i just got it i was substituting wrong thanks for the help