Final answer:
The focus is on evaluating the truth of statements related to linear algebra, particularly systems of equations ax=b, using knowledge of matrix operations and the importance of listing known values for solving these problems.
Step-by-step explanation:
The student's question concerns the system of linear equations ax = b, where 'a' is an n×n matrix and 'b' is a non-zero vector in Rn. They are tasked with determining the truthfulness of statements related to these equations, which indicates a focus on linear algebra. To correctly answer such questions, one must evaluate the givens and use knowledge of matrix operations and properties. For example, if A × F = B × F and F is non-zero, we cannot conclusively say that A = B unless F is an invertible matrix. Similarly, for two linear equations to be equivalent, their respective isolation of the same constant does not guarantee equality unless other conditions are met. To solve such problems, it's helpful to list all known values and correctly identify what needs to be solved.