Linear Algebra and Its Applications · Problem 8.2.9

Linear Programming and Game Theory — Gilbert Strang

Mathematics · simplex-method-product-form-inverse

Problem

Verify the inverse in equation (5), and show that

BE

has

Bv = u

in its

k

th column. Then

BE

is the correct basis matrix for the next stop,

E^{-1}B^{-1}

is its inverse, and

E^{-1}

updates the basis matrix correctly.