TheWrathOfMath
Junior Member
- Joined
- Mar 31, 2022
- Messages
- 162
Prove or disprove:
B is a square matrix. There exists an invertible matrix A so that AB is an upper triangular matrix.
I know that this is a true statement, since I managed to find matrices A and B that satisfy the condition.
However, I do not know how to write a proof for the general case.
I know that every matrix in row echelon form is upper triangular.
I also know that there exists a finite number of elementary matrices that when multiplied by A will yield a matrix which is upper triangular: E1...Ek*A (basically the same as performing elementary row operations on A in order to transform it into row echelon form).
Assistance would be highly appreciated.
B is a square matrix. There exists an invertible matrix A so that AB is an upper triangular matrix.
I know that this is a true statement, since I managed to find matrices A and B that satisfy the condition.
However, I do not know how to write a proof for the general case.
I know that every matrix in row echelon form is upper triangular.
I also know that there exists a finite number of elementary matrices that when multiplied by A will yield a matrix which is upper triangular: E1...Ek*A (basically the same as performing elementary row operations on A in order to transform it into row echelon form).
Assistance would be highly appreciated.