Wrong Answer Notes MA207

Use the top most line of matrix to find echelon form. Take away multiple of it from all other lines.

Double check signs.

If x is an eigenvector of M, then Mx will be a scalar multiple of x with the multiple being the corresponding eigenvector.

3x3 matrix inverse. Remember to transpose the cofactor matrix. Video below.

https://www.youtube.com/watch?v=g7TFJUJXErU

If the quadratic equation is in symmetrical matrix form then use the matrix method of finding stationary points

If not then use the other method(week 10 method) of finding stationary points

Orthogonal matrix is the unit eigenvectors of eigenvalues put together

Remember x = Pz/x = Pu always

Row operations = use matrices

If all principal minors and eigenvalues are positive, then the equation is positive definite

2014 Summer
 * multiply eigenvector by matrix to see if eigenvector. scalar multiple result means eigenvector. the scalar multiple is the eigenvalue
 * convert eigenvectors to unit vectors then put them into P
 * always x = Pu
 * find the lambda
 * find the contract curve using the utility curves equate hessian and find lambda
 * don't forget about finite quantity of goods in the utility curve
 * put bundle in contract curve to see if it is optimal
 * use quantities to find the equation connecting the two goods
 * differentiating x=Pu version questions are not too different
 * use e^x instead
 * alternating signs or only + signs on principal minors matter
 * directional directive is unit vector of point x gradient vector subbed with point