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