ECON 2141 Part 3
cofactor matrix
A matrix with elements that are the cofactors, term-by-term, of a given square matrix.
cramer's rule
a method that uses determinants to solve a system of linear equations
the first order condition is a what condition? (necessary/sufficient,etc)
a necessary condition for x* to be an interior max or min, but not a sufficient condition
what is the hessian
a special matrix where the elements are the second order partial derivatives of a function it can be used to evaluate the function's concavity around the critical points neighborhoods
how to perform constrained optimization using the hessian
find the bordered hessian
look @ question on the back and maximize the profit function
profit function is: Q1(40-4Q1)+Q2(98-10Q2)-(80+8(Q1+Q2))
x_1 + 2x_2 = 2 2x_1+4x_2 = 4 unique soln?
the two lines coincide - there are infinite solutions
if a matrix is invertible what is its inverse
A^-1
look @ question on back and find inverse matrix
X = A^(-1)b = [4 2.5]
what is a minor of a matrix |M_{ij}|
determinant of the matrix left when row i and column j have been deleted
what is the sufficient condition to find extreme points
evaluate the second order partial derivatives. this is done using the hessian
when is a square matrix invertible
if and only if it is nonsingular
steps to solve for unknowns in a linear system using matrices
make coefficient matrix check that it is non singluar (ie find determinant) find the cofactor matrix find the adjoint matrix find the inverse matrix
square matrix
n x n dimensions
x_1 + 2x_2 = 3 2x_1+4x_2 = 4 unique soln?
no the lines are parralel and never concide so no unique soln
