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Lesson: Reduced Echelon Form

In this lesson, we will learn how to reduce a matrix to obtain its row-reduced echelon form.

Worksheet • 6 Questions

Q1:

Is the following matrix in the reduced echelon form?

  • Ayes
  • Bno

Q2:

Transform the following matrix to row-reduced echelon form.

  • A 1 0 0 3 0 1 0 0 0 0 1 − 2
  • B 1 0 0 3 0 1 0 1 0 0 1 − 2
  • C 1 0 0 1 0 1 0 0 0 0 1 0
  • D 1 0 0 3 0 1 0 0 0 0 0 − 2
  • E 1 0 0 1 0 1 0 0 0 0 0 0

Q3:

Is the following matrix in the reduced echelon form?

  • Ano
  • Byes

Q4:

Is the following matrix in row-reduced echelon form?

  • Ano
  • Byes

Q5:

Reduce the following matrix to obtain its row-reduced echelon form, and then list the pivot columns.

  • A , pivot columns: 1, 2, and 4
  • B , pivot columns: 1, 2, and 3
  • C , pivot columns: 1, 3, and 4
  • D , pivot columns: 2, 3, and 4
  • E , pivot columns: 1, 2, 3, and 4

Q6:

Reduce the following matrix to obtain its row-reduced echelon form, and then list the pivot columns.

  • A , pivot columns: 1, 2, and 3
  • B , pivot columns: 1 and 2
  • C , pivot columns: 1 and 2
  • D , pivot columns: 1, 2, and 3
  • E , pivot columns: 1, 2, and 3
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