Solving system of equations using inverse of coefficient matrix

[whispyr]

x-3y-2z=8
-2x+7y+3z=-19
x-y-3z=3

i've worked it out using the determinants to be x=4, y=-2, and z=1.
But my teacher said i'm using the wrong way to solve this equation and have no idea how to use the coefficient matrix?
Any help would be greatly appreciated

edit:
I got the inverse divided it by the determinant and got

[-18 -7 5]
[-3 -1 1]
[-5 -2 -1]
-18(8)-7(-19)+5(3)=4
X=4
-3(8)-1(-19)+1(3)=-2
Y=-2
-5(8)-2(-19)+1(3)=1
Z=1

but she says i'm not using the right coefficient matrix? I'm a bit confused here. Are the values that I got wrong?

edit edit: just showing the work I did to get to my answer

[1 -3 -2] [x]=[8]
[-2 7 3] [y ]=[-19]
[1 -1 -3] [z]=[3]
1[7 3]+3[-2 3]+2[-2 7]
[-1 -3] [1 -3] [1-1]
1(-18)+3(3)-2(-5)
Det=1
[
+[7 3]-[-2 3]+[-2 7]
[-1 -3] [1 -3][1-1]
-[-3 -2]+[1 -2]-[1 -3]
[-1 -3] [1-3] [1-1]
+[-3 -2] – [1-2] + [1-3]
[7 3] [-2 3] [-2 7]
]

[-18 -3 -5]
[-7 -1 -2]
[5 1 1]

1[-18 -7 5]
[-3 -1 1]
[-5 -2 -1]

 

[pka]

x-3y-2z=8
-2x+7y+3z=-19
x-y-3z=3

\(\displaystyle {\left( {\begin{array}{*{20}{c}} 1&{ - 3}&{ - 2} \\
{ - 2}&7&3 \\
1&{ - 1}&{ - 3}
\end{array}} \right)^{ - 1}} = \left( {\begin{array}{*{20}{c}}
{ - 18}&{ - 7}&5 \\
{ - 3}&{ - 1}&1 \\
{ - 5}&{ - 2}&1
\end{array}} \right)\)

 

[mmm4444bot]

x - 3y - 2z = 8

-2x + 7y + 3z = -19

x - y - 3z = 3

X = 4

Y = -2

Z = 1

Are the values that I got wrong?

No. You have the correct solution, and you could verify this yourself by substituting your solution candidates into the original system and then ensuring that they all lead to true statements.

Your symbols X,Y,Z are not correct, however.

Do not interchange upper- and lower-case letters to represent the same number. Stick with the symbols that are given.

she says i'm ntot using the right coefficient matrix

[1 -3 -1]
[-2 7 3]
[1 -1 -3]

Well, she's right because one of the elements in the matrix above is wrong.

I think I saw another wrong value in a matrix, elsewhere in your post.

Compare what you write down on paper with the given system; that is, proofread your work.

Also, if you continue posting about this exercise, please include the exact instructions that you received with this exercise.

Cheers :cool:

 

[whispyr]

I'm a bit confused I did the work to get the x,y,z values but I guess its not the right way to do it? Confused a bit

 

[mmm4444bot]

I note that you did not follow my specific instruction to you.

:idea: Maybe your difficulty lies in not following instructions.

 

[whispyr]

the exact instruction that was given is in the title, but for your sake I will type it out. "Solve the system of equations using the inverse of the coefficient matrix"

if you included any other subtle hints they went unnoticed.

 

[mmm4444bot]

Thank you for responding to my instruction and for clarifying the exact instructions that you received from your teacher. You may now wait for somebody else to assist you further. Cheers :cool: