- #1

- 29

- 0

Consider a matrix A, and let B = rref(A).

Is ker(A) necesarily equal to ker(B), and is im(A) necessarily equal to im(B)?

I want to say that the answer to both questions are yes because A and B are the same matrix, i.e. there are a finite number of elementary operations that can change A to B, and vice versa. Therefore, if they are the same matrices, then they necessarily will have the same kernel and image as each other.

Is my reasoning correct?

Is ker(A) necesarily equal to ker(B), and is im(A) necessarily equal to im(B)?

I want to say that the answer to both questions are yes because A and B are the same matrix, i.e. there are a finite number of elementary operations that can change A to B, and vice versa. Therefore, if they are the same matrices, then they necessarily will have the same kernel and image as each other.

Is my reasoning correct?

Last edited: