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CH 1 T/F Exam Questions And Answers
100% Guaranteed Pass.
Every matrix is row equivalent to a unique matrix in echelon form. - Answer✔False, reduced
echelon form
Any system of n linear equations in n variable has at most n solutions. - Answer✔False, Let A be
any n×n matrix with fewer than n pivot columns. Then the equation Ax = 0 has infinitely many
solutions
If a system of linear equations has two different solutions, it must have infinitely many solutions.
- Answer✔True
If a system of linear equations has no free variables, then it has a unique solution. -
Answer✔False, could have no free variables and no solution
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 sets. - Answer✔True
If a system Ax=b has more than one solutions, then so does the system Ax=0. - Answer✔True
If A is an m x n matrix and the equation Ax=b is consistent for some b, then the columns of A
span R^m. - Answer✔False, For the columns of A to span R^m, the equation Ax=b must be
consistent for all b in R^m, not for just one vector b in R^m
If an augmented matrix [A b] can be transformed by elementary row operations into echelon
form, then the equation Ax=b is consistent. - Answer✔False, any matrix can be transformed by
elementary row operations into reduced echelon form, but not every matrix equation Ax = b is
consistent
If matrices A and B are row equivalent, they have the same reduced echelon form. -
Answer✔True
The equation Ax=0 has the trivial solution if and only if there are no free variables. -
Answer✔False, every equation Ax = 0 has the trivial solution
If A is an m x n matrix and the equation Ax=b is consistent for every b in R^m, then A has m
pivot positions. - Answer✔True
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CH 1 T/F Exam Questions And Answers
100% Guaranteed Pass.
Every matrix is row equivalent to a unique matrix in echelon form. - Answer✔False, reduced
echelon form
Any system of n linear equations in n variable has at most n solutions. - Answer✔False, Let A be
any n×n matrix with fewer than n pivot columns. Then the equation Ax = 0 has infinitely many
solutions
If a system of linear equations has two different solutions, it must have infinitely many solutions.
- Answer✔True
If a system of linear equations has no free variables, then it has a unique solution. -
Answer✔False, could have no free variables and no solution
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 sets. - Answer✔True
If a system Ax=b has more than one solutions, then so does the system Ax=0. - Answer✔True
If A is an m x n matrix and the equation Ax=b is consistent for some b, then the columns of A
span R^m. - Answer✔False, For the columns of A to span R^m, the equation Ax=b must be
consistent for all b in R^m, not for just one vector b in R^m
If an augmented matrix [A b] can be transformed by elementary row operations into echelon
form, then the equation Ax=b is consistent. - Answer✔False, any matrix can be transformed by
elementary row operations into reduced echelon form, but not every matrix equation Ax = b is
consistent
If matrices A and B are row equivalent, they have the same reduced echelon form. -
Answer✔True
The equation Ax=0 has the trivial solution if and only if there are no free variables. -
Answer✔False, every equation Ax = 0 has the trivial solution
If A is an m x n matrix and the equation Ax=b is consistent for every b in R^m, then A has m
pivot positions. - Answer✔True
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