Row Echelon Calculator

The Row Echelon Form Calculator allows users to input a matrix and select decimal precision to obtain its row echelon form, rank, leading entries, and the elementary row operations used in the process.

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How to Use the Row Echelon Form Calculator

This guide will walk you through the steps to use the Row Echelon Form Calculator to transform any given matrix into its row echelon form, determine its rank, and obtain other useful information.

Step 1: Set Matrix Dimensions

Begin by specifying the size of the matrix you wish to work with. The calculator requires you to enter:

  • Number of Rows: Enter a whole number between 1 and 5 in the “Number of Rows” field. This value indicates how many rows the matrix will have.
  • Number of Columns: Enter a whole number between 1 and 6 in the “Number of Columns” field. This value indicates how many columns the matrix will have.

Both fields are required, and the input must be within the specified ranges.

Step 2: Select Decimal Precision

Next, choose the level of precision you want for the calculated numbers. In the “Decimal Precision” dropdown menu, select one of the available options:

  • 2 decimal places
  • 3 decimal places
  • 4 decimal places

This setting will determine how the numbers in the row echelon form matrix and other computed results are displayed.

Step 3: Input the Matrix

Once the dimensions and precision are set, input the elements of the matrix corresponding to the size you specified. Ensure all entries are provided in your matrix.

Step 4: Generate the Row Echelon Form

With all inputs in place, proceed to calculate the row echelon form. The calculator will apply elementary row operations to transform your matrix and will display the following results:

  • Row Echelon Form: The resulting matrix in row echelon form, formatted according to the decimal precision selected.
  • Matrix Rank: The rank of the matrix which is determined by counting the number of leading entries in its row echelon form.
  • Leading Entries: A count of the non-zero leading entries in the row echelon matrix, which are pivotal in determining the matrix’s rank.
  • Elementary Row Operations: A step-by-step record of the operations performed to achieve the row echelon form, detailing the transformations applied.

Review the output to ensure that it matches the expectations and use it to analyze the properties of the given matrix.