TRUE OR FALSE 7 If A and B are matrices with the same row re

TRUE OR FALSE

7. If A and B are matrices with the same row reduced echelon form, then the system A~x = 0 and B~x = 0 have the same number of solutions.
8. If A and B are matrices with the same row reduced echelon form, then the system A~x = ~b and B~x = ~b have the same number of solutions.
9. If a matrix E is in row reduced echelon form and we omit one column, then the remaining matrix is also in row reduced echelon form.

Solution

7.The statement is TRUE as the linear system of equations represented by Ax = 0 and Bx = 0 woud be identical.

8. The statement is TRUE as the linear system of equations represented by Ax = b and Bx = b woud be identical.

9. The statement is TRUE.

Reason: The following are the properties of the reduced echelon form of a matrix: