Linear Algebra and Its Applications · Problem 1.2.3

Matrices and Gaussian Elimination — Gilbert Strang

Mathematics · geometry-of-linear-equations

Problem

(Recommended) Describe the intersection of the three planes

u+v+w+z = 6

and

u+w+z = 4

and

u+w = 2

(all in four-dimensional space). Is it a line or a point or an empty set? What is the intersection if the fourth plane

u = -1

is included? Find a fourth equation that leaves us with no solution.