In some​ cases, a matrix may be row reduced to an ext than one procession in decreased echelon​ form, using different sequences of heat operations.Is this statement true or​ false?
The heat reduction algorithm uses only come augmented matrices because that a linear system.Is this declare true or​ false?
The statement is false. The algorithm applies to any​ matrix, even if it is or not the procession is viewed as an augmented matrix for a straight system.

You are watching: The echelon form of a matrix is unique. choose the correct answer below.

A basic variable in a direct system is a change that synchronizes to a pivot tower in the coefficient matrix.Is this statement true or​ false?
Finding a parametric summary of the solution collection of a direct system is the same as addressing the system.Is this statement true or​ false?
The statement is false. The solution collection of a direct system have the right to only be expressed utilizing a parametric summary if the system contends least one solution.
The explain is false. The echelon type of a matrix is not​ unique, yet the reduced echelon form is unique.
The pivot location in a matrix count on whether row interchanges are provided in the heat reduction process. Choose the correct answer below.
The statement is false. The pivot location in a matrix space determined fully by the positions of the top entries in the nonzero rows of any echelon type obtained native the matrix.
Reducing a procession to echelon form is dubbed the forward phase of the row reduction process. Choose the exactly answer below.
The declare is true. To reduce a procession to echelon kind is dubbed the forward phase and reducing a procession to reduced echelon kind is referred to as the behind phase.
Whenever a system has free​ variables, the solution set contains numerous solutions. Select the correct answer below.
The explain is false. The presence of at the very least one equipment is not related to the presence or absence of totally free variables. If the device is​ inconsistent, the solution set is empty.
A general solution the a system is one explicit description of all solutions of the system. Choose the exactly answer below.
The statement is true. The heat reduction algorithm leads directly to an explicit summary of the solution set of a direct system as soon as the algorithm is applied to the augmented procession of the​ system, resulting in a basic solution that a system.
Suppose the coefficient matrix of a system of straight equations has actually a pivot place in every row. Define why the system is consistent
The device is consistent since the rightmost column of the augmented procession is no a pivot column.
A system of direct equations with fewer equations than unknowns is sometimes referred to as an underdetermined system. Deserve to such a system have actually a unique​ solution? Explain.

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No, that cannot have actually a unique solution. Because there are an ext variables than​ equations, there must be at the very least one free variable. If the linear system is consistent and also there is at least one free​ variable, the solution collection contains infinitely countless solutions. If the straight system is​ inconsistent, over there is no solution.
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Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications come Differential Equations and Probability2nd EditionTom M. Apostol
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