16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 5.4.11

Determinants

Mathematics — Linear Algebra · invertibility-linear-combination

Problem

Let

A

and

B

n \times n

matrices over the field

F

. Show that if

A

is invertible there are at most

n

scalars

c

F

for which the matrix

cA + B

is not invertible.