Linear Algebra Done Right · Problem 9C.2

Operators on Real Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · determinants

Problem

Suppose the first column of a square matrix

A

consists of all zeros except possibly the first entry

A_{1,1}

. Let

B

be the matrix obtained from

A

by deleting the first row and the first column of

A

. Show that

\det A = A_{1,1} \det B