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Linear Algebra Final ReviewChapter 11. Every matrix is row equivalent to a unique matrix in echelon form. False because you can row reduce a matrix into a multitude of ways, row reducing it to its pure RREF or just to a triangular reduction. 2. Any system of n linear equations in n variables has at most n solutions. False because in an nxn matrix, there can be a row of zeros, indicating a free variable; hence, there can exist infinitely many solutions to the system of linear equations. 3. If a system of linear equations has two different solutions, it must have infinitely many solutions. True because if the system has more than one unique solution, the system suggests that there is a free variable; hence, there will exist infinitely many solutions.4. If a system of linear equations has no free variables, then it has a unique solution. False; even when there exist no free variables, that doesnt mean the complement is true; that is, there doesnt exist a unique solution nor are there signs of basic variables. The system may be inconsistent.5. If an augmented matrix [A b] is transformed into [C d] by elementary row operations, then the equations Ax=b and Cx=d have exactly the same solution. True because by definition and by the properties of row reduction, a matrix that has been row reduced n-number of times maintains its row equivalency with its previous matrix form; hence, the solution that may be difficult to see from Ax=b is, nonetheless, the same as the soluti

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