Question

Is it possible for a singular matrix B to be row equivalent to a nonsingular matrix A? Explain.

Answer 1

no

Answer 2

let B a singular matrix row equivalent to A (nonsingular).

then there is a sequence E1,...,En of elemtary matrices sucn that
En*...*E1*B=A
from this it would follow that
B=E1^-1*...*En^-1*A
but then B would invertible, a contradiction.

Answer 3

great, tyvm.