A First Course in Linear Algebra · Problem T12

Systems of Linear Equations — Robert Beezer

Mathematics — Linear Algebra · submatrix-rref

Problem

Suppose that

B

is an

m \times n

matrix in reduced row-echelon form. Build a new, likely smaller,

k \times \ell

matrix

C

as follows. Keep any collection of

k

adjacent rows,

k \leq m

. From these rows, keep columns 1 through

\ell

\ell \leq n

. Prove that

C

is in reduced row-echelon form.