# Thread: Using a result to find solution to a system.

1. ## Using a result to find solution to a system.

Ok so for the first part of this question I was required to find the inverse of A =

(1 3 3)
(1 4 3)
(1 3 4)

I did this and got:

(1 0 0)
(0 1 0)
(0 0 1)

Now I am required to "use result from first part" to find the solution to this system:

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

Would I substitute x=1, y=1, z=1? I am not sure at all what to do

2. ## Re: Using a result to find solution to a system.

Originally Posted by kmjt
Ok so for the first part of this question I was required to find the inverse of A =

(1 3 3)
(1 4 3)
(1 3 4)

I did this and got:

(1 0 0)
(0 1 0)
(0 0 1)

Now I am required to "use result from first part" to find the solution to this system:

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

Would I substitute x=1, y=1, z=1? I am not sure at all what to do
$\displaystyle \left[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix}\right]$ is NOT the inverse of $\displaystyle \left[\begin{matrix}1&3&3 \\ 1&4&3\\ 1 & 3 & 4\end{matrix}\right]$, it is the identity matrix. An inverse matrix is defined to be the matrix you multiply by to GET to the identity matrix.