Summary: Oefenvragen

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• 1 oefenvragen

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• every elementary row operation is reversible

  true, (see the remarks following the box titled Elementary Row Operations 1.1

•  a 5 x 6 matrix has six rows

   false, a 5x6 matrix has five rows 1.1

•  two matrices are row equivalent if they have the same number of rows

   false, the definition of row equivalent requires that there exist a sequence of row operations that transforms one matrix into the other 1.1

•  elementary row operations on an augmented matrix never change the solution set of the associated linear system

   true, (see the box preceding the subsection titled  existence and uniqueness questions) 1.1

•  two equivalent linear systems can have different solution sets

   false, the definition of equivalent systems is in the second paragraph after equation 2 1.1

•  in some cases, a matrix may be row reduced to more than one matrix in reduced echelon form, using different sequences of row operations

   false, see theorem 1   1.2

•  the row reduction algorithm applies only to augmented matrices for a linear system

   false, see the second paragraph of the section 1.2

•  a basic variable in a linear system is a variable that corresponds to a pivot column in the coefficient matrix

   true, basic variables are defined after equation 4 1.2

•  finding a parametric description of the solution set of a linear system is the same as solving the system 

   true, this statement is at the beginning of parametric descriptions of solutions sets 1.2

•  if one row in an echelon form of an augmented matrix is (0 0 0 5 0) then the associated linear system is inconsistent

   false, the row shown corresponds to the equation 5*X4=0 which does not by itself lead to a contradiction. so the system might be consistent or it might be inconsistent 1.2