1. ## finding general algorithm

it says that i need to find a general algorithm for solving determinants if matrices using minors of the first row for matrices larger than 2x2.

I also need to do the same thing for solving a system of n linear quations with n independent variables using determinants.

I know how to solve for both... but i'm having trouble writing a gereal algorithm for it.

thank you sooo much

2. Originally Posted by jumpingpanda
it says that i need to find a general algorithm for solving determinants if matrices using minors of the first row for matrices larger than 2x2.

I also need to do the same thing for solving a system of n linear quations with n independent variables using determinants.

I know how to solve for both... but i'm having trouble writing a gereal algorithm for it.

thank you sooo much

i'll put the first one this way:

Let A be the nxn matrix.
represent the Minor of the first row by $\displaystyle det (M_{1,j}) = |M_{1,j}|$ where $\displaystyle M_{1,j}$ is the (n-1)x(n-1) matrix obtained by deleting the first row and the jth column, j runs from 1 to n.

det A = $\displaystyle a_{1,1}(-1)^{1+1}|M_{1,1}| + a_{1,2}(-1)^{1+2}|M_{1,2}| + ... + a_{1,n}(-1)^{1+n}|M_{1,n}| = \displaystyle\sum_{j=1}^n a_{1,j}(-1)^{1+j}|M_{1,j}|$