Matrix Rank Calculator

The Matrix Rank Calculator helps users to input matrix dimensions and elements, calculates the matrix rank, determinant, and determines if the matrix is invertible, supporting matrix types including general, symmetric, and diagonal up to 5×5.

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Step-by-Step Guide to Using the Matrix Rank Calculator

Introduction

This Matrix Rank Calculator assists in determining the rank, determinant, and invertibility of a matrix. Follow these steps for the effective use of this calculator to analyze your matrix.

Step 1: Enter the Number of Rows

  • Locate the input field labeled Number of Rows.
  • Input the desired number of rows in the matrix, ensuring it is between 1 and 5. Use whole numbers only as specified by the step validation.

Step 2: Enter the Number of Columns

  • Find the input field labeled Number of Columns.
  • Enter the desired number of columns, making sure the value is between 1 and 5, adhering to whole numbers.

Step 3: Select the Matrix Type

  • Go to the Matrix Type dropdown menu.
  • Choose the appropriate type of matrix: General Matrix, Symmetric Matrix, or Diagonal Matrix.

Step 4: Input Matrix Elements

  • Fill in the specified fields for each matrix element:
  • Element (1,1): Input the value for the first row, first column.
  • Element (1,2): Enter the value for the first row, second column.
  • Element (2,1): Provide the value for the second row, first column.
  • Element (2,2): Type in the value for the second row, second column.
  • Ensure all fields are filled, following correct validation requirements.

Step 5: Calculate the Rank, Determinant, and Invertibility

  • Upon filling all required fields, the calculator will compute the following:
  • Matrix Rank: Displayed in whole numbers.
  • Determinant: Calculated as (element11 * element22) – (element12 * element21), presented to two decimal places.
  • Is Matrix Invertible: Shows Yes if the determinant is not 0, otherwise No.

Conclusion

By following these steps, you can effectively use the Matrix Rank Calculator to gain valuable insights into your matrix’s properties. Ensure all data entries are valid for accurate calculations.