So, Cramer's Rule solves linear equations. and it expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one column by the vector of right hand sides of the equations.
for example:
ax+by+cz=j
dx+ey+fz=k
gx+hy+iz=l
the coefficient matrix would be [[a,b,c][d,e,f][g,h,i]] and the matrix for the variable x is [[j,b,c][k,e,f][l,h,i]], the matrix for variable y is [[a,j,c][d,k,f][g,l,i]], the matrix for variable z is [[a,b,j][d,e,k][g,h,l]]
to find the solutions to the variables would be the following:
Det( X matrix)/Det( Co-eff matrix) = X
Det( Y matrix)/Det( Co-eff matrix) = Y
Det( Z matrix)/Det( Co-eff matrix) = Z
the calculator comes built in with det so that saves you a ton of work already. you can create a matrix just using the [ and the ].
but there is a easier way to solve for linear equations, the rref where you just put practically everything into just one matrix and your output is on the last column output.
