Originally Posted by

**Beard** Hi, I'm having a problem finding the inverse of a matrix in that I have no idea where I am going wrong. I am given two simultaneous equations and told to find the inverse of A and therefore determine the value of x.

$\displaystyle 2x_1 + 3x_2 = 1\ and\ x_1 + 7x_2 = 6 $. I have put this in the form Ax = b as asked by the question.

$\displaystyle \left[\begin{array}{cc}2&3\\1&7\end{array}\right] \left[\begin{array}{c}x_1\\x_2\end{array}\right] = \left[\begin{array}{c}1\\6\end{array}\right]$.

I know that if I multiply both sides by the inverse I get $\displaystyle x = A^{-1}b$. To find the inverse from here $\displaystyle A^{-1} = \frac{1}{det(A)}\cdot A_{cof}T$ (where the T is for transposed).

So $\displaystyle A = \left[\begin{array}{cc}2&3\\1&7\end{array}\right] \ \ A_{cof} = \left[\begin{array}{cc}2&-1\\-3&7\end{array}\right] \ \ A_{cof}T = \left[\begin{array}{cc}2&-3\\-1&7\end{array}\right]$

I calculated the det(A) as being 11 (14 -3) so $\displaystyle A^{-1} = \frac{1}{11} \cdot \left[\begin{array}{cc}2&-3\\-1&7\end{array}\right]$

If something hasn't already gone wrong then here is where it doesn't make sense from me. Just to make sure that it was correct I decided to multiply A by the inverse I just got and to see if I got the identity matrix. I didn't. Can anyone help me in finding where I have gone wrong. I can do the rest from there

Thanks