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Linear Algebra 1.2 Exam Study Guide.
Reduced Echelon Form -
Echelon Form -
Neither -
- Answer✔The system is consistent, with a unique solution
- Answer✔The system is inconsistent.
In some cases, a matrix may be row reduced to more than one matrix in reduced echelon form,
using different sequences of row operations.
Is this statement true or false? - Answer✔The statement is false. Each matrix is row equivalent to
one and only one reduced echelon matrix
The row reduction algorithm applies only to augmented matrices for a linear system.
Is this statement true or false? - Answer✔The statement is false. The algorithm applies to any
matrix, whether or not the matrix is viewed as an augmented matrix for a linear system.
A basic variable in a linear system is a variable that corresponds to a pivot column in the
coefficient matrix.
Is this statement true or false? - Answer✔The statement is true. It is the definition of a basic
variable.
Your answer is correct.
Finding a parametric description of the solution set of a linear system is the same as solving the
system.
Is this statement true or false? - Answer✔The statement is false. The solution set of a linear
system can only be expressed using a parametric description if the system has at least one
solution.
The echelon form of a matrix is unique. Choose the correct answer below - Answer✔The
statement is false. The echelon form of a matrix is not unique, but the reduced echelon form is
unique.
1|Page
Linear Algebra 1.2 Exam Study Guide.
Reduced Echelon Form -
Echelon Form -
Neither -
- Answer✔The system is consistent, with a unique solution
- Answer✔The system is inconsistent.
In some cases, a matrix may be row reduced to more than one matrix in reduced echelon form,
using different sequences of row operations.
Is this statement true or false? - Answer✔The statement is false. Each matrix is row equivalent to
one and only one reduced echelon matrix
The row reduction algorithm applies only to augmented matrices for a linear system.
Is this statement true or false? - Answer✔The statement is false. The algorithm applies to any
matrix, whether or not the matrix is viewed as an augmented matrix for a linear system.
A basic variable in a linear system is a variable that corresponds to a pivot column in the
coefficient matrix.
Is this statement true or false? - Answer✔The statement is true. It is the definition of a basic
variable.
Your answer is correct.
Finding a parametric description of the solution set of a linear system is the same as solving the
system.
Is this statement true or false? - Answer✔The statement is false. The solution set of a linear
system can only be expressed using a parametric description if the system has at least one
solution.
The echelon form of a matrix is unique. Choose the correct answer below - Answer✔The
statement is false. The echelon form of a matrix is not unique, but the reduced echelon form is
unique.
1|Page
