Linear Algebra 1.2

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question
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?
The statement is false. Each matrix is row equivalent to one and only one reduced echelon matrix
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The row reduction algorithm applies only to augmented matrices for a linear system. Is this statement true or? false?
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.
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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?
The statement is true. It is the definition of a basic variable. Your answer is correct.
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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?
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.
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The echelon form of a matrix is unique. Choose the correct answer below
The statement is false. The echelon form of a matrix is not? unique, but the reduced echelon form is unique.
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The pivot positions in a matrix depend on whether row interchanges are used in the row reduction process. Choose the correct answer below.
The statement is false. The pivot positions in a matrix are determined completely by the positions of the leading entries in the nonzero rows of any echelon form obtained from the matrix.
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Reducing a matrix to echelon form is called the forward phase of the row reduction process. Choose the correct answer below.
The statement is true. Reducing a matrix to echelon form is called the forward phase and reducing a matrix to reduced echelon form is called the backward phase.
question
Whenever a system has free? variables, the solution set contains many solutions. Choose the correct answer below.
The statement is false. The existence of at least one solution is not related to the presence or absence of free variables. If the system is? inconsistent, the solution set is empty.
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A general solution of a system is an explicit description of all solutions of the system. Choose the correct answer below.