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1.2 Row Reduction and Echelon Forms Exam with Questions and Answers
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1.2 Row Reduction and Echelon Forms Exam with Questions and Answers A rectangular matrix is in echelon form if it has the following 3 properties: ANSWER All nonzero rows are above any rows of all zeros; each leading entry of a row is in a column to the right of the leading entry of the row above...

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  • May 16, 2024
  • 3
  • 2023/2024
  • Exam (elaborations)
  • Questions & answers

Subjects

  • 12 row reduction and echelon forms exam q and a
  • a rectangular matrix is in echelon form if it has
  • each matrix is row equivalent to

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  • Echelon
  • Echelon

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1.2 Row Reduction and Echelon Forms Exam with Questions and Answers
A rectangular matrix is in echelon form if it has the following 3 properties: ANSWER All nonzero rows are above any rows of all zeros; each leading entry of a row is in a column to the right of the leading entry of the row above it; all entries in a column below a leading entry
are zeros.
leading entry ANSWER leftmost nonzero entry in a nonzero row
If a matrix in echelon form satisfies the following additional conditions, then it is in reduced echelon form ANSWER the leading entry in each nonzero row is 1; each leading 1 is the only
nonzero entry in its column.
Each matrix is row equivalent to... ANSWER one and only one reduced echelon matrix
Since the reduced echelon form is unique, the leading entries are... ANSWER always in the same positions in any echelon form obtained from a given matrix
Pivot position ANSWER a location in a matrix that corresponds to a leading 1 in the reduced echelon form of a matrix.
Pivot column ANSWER column of a matrix that contains a pivot position
pivot ANSWER nonzero number in a pivot position that is used as needed to create zeros via row operations.

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