Linear Algebra and Its Applications · Problem 2.5.4

Vector Spaces — Gilbert Strang

Mathematics · graphs-and-networks

Problem

Compute the 3 by 3 matrix

A^T A

, and show that it is symmetric but singular—what vectors are in its nullspace? Removing the last column of

A

(and last row of

A^T

) leaves the 2 by 2 matrix in the upper left corner; show that it is not singular.