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Lesson Worksheet: Reduced Row Echelon Form Mathematics

In this worksheet, we will practice identifying the reduced row echelon form of a matrix and using Gauss-Jordan elimination to get it and hence solving a system of linear equations.

Q1:

Describe the row switches which are necessary to put the following matrix into echelon form: 034000222004.

  • AWe swap rows 1 and 3, and then rows 2 and 4.
  • BThe matrix is already in echelon form; we do not need to swap any rows.
  • CWe swap rows 1 and 3, and then rows 2 and 4, and finally rows 3 and 4.
  • DWe swap rows 2 and 4, and then rows 2 and 1, and finally rows 2 and 3.
  • EWe swap rows 2 and 4, and then rows 1 and 3, and finally rows 2 and 3.

Q2:

Give the sum of all the pivot entries in the following matrix: 𝐴=351000004001120.

Q3:

State whether the following matrix is in echelon form: 054024002.

  • AThe matrix is in echelon form.
  • BThe matrix is not in echelon form.

This lesson includes 2 additional questions for subscribers.

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