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Worksheet: Reduced Echelon Matrices

Q1:

Is the matrix 1 2 0 0 1 7 in the reduced echelon form?

  • ANo
  • BYes

Q2:

Transform the following matrix to row-reduced echelon form.

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

Q3:

Is the matrix in the reduced echelon form?

  • AYes
  • BNo

Q4:

Is the matrix in row-reduced echelon form?

  • AYes
  • BNo

Q5:

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

  • A 1 0 0 0 0 1 1 0 0 0 0 1 , pivot columns: 1, 2, 3, and 4
  • B 1 0 0 0 0 2 1 0 0 0 0 1 , pivot columns: 1, 3, and 4
  • C 1 0 0 1 0 1 1 0 0 0 0 1 , pivot columns: 2, 3, and 4
  • D 1 0 0 0 0 1 0 . 5 0 0 0 0 1 , pivot columns: 1, 2, and 4
  • E 1 0 0 0 0 1 1 0 0 1 0 1 , pivot columns: 1, 2, and 3

Q6:

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

  • A 1 0 0 0 1 0 0 0 1 0 0 1 , pivot columns: 1, 2, and 3
  • B 1 0 0 0 1 1 0 0 0 0 0 1 , pivot columns: 1 and 2
  • C 1 0 0 0 1 0 0 0 1 1 0 0 , pivot columns: 1, 2, and 3
  • D 1 0 0 0 1 0 0 0 1 0 0 0 , pivot columns: 1, 2, and 3
  • E 1 0 0 0 1 1 1 0 1 0 0 0 , pivot columns: 1 and 2