Evaluate (
2 3 1
0 1 5
3 7 2
)^-1 17 by doing row reduct

Question

Evaluate (
    2     3     1 
     0     1     5 
     3     7     2
)^-1 17 by doing row reduct

Accepted Answer

Step 1:u000AStart with the augmented matrix:u000A$$u000Au005Cleft(u005Cbegin{array}{ccc|ccc}u000A2 u0026 3 u0026 1 u0026 1 u0026 0 u0026 0 u005C

Evaluate $$ \left(\begin{array}{lll} 2 & 3 & 1 \\ 0 & 1 & 5 \\ 3 & 7 & 2 \end{array}\right)^{-1} \bmod 17 $$ by doing row reduction modulo 17 on the augmented matrix $$ \left(\begin{array}{llllll} 2 & 3 & 1 & 1 & 0 & 0 \\ 0 & 1 & 5 & 0 & 1 & 0 \\ 3 & 7 & 2 & 0 & 0 & 1 \end{array}\right) $$