Inverse of a Matrix in Excel Find the inverse of matrix using Excel

Inverse of a Matrix in Excel Find the inverse of matrix using Excel. Use the directions from “excel spreadsheet” in your book to calculate. Explain all steps in a Word document. -751 2 30-21 -56-20 203-2 A=

The Correct Answer and Explanation is :

To find the inverse of a matrix in Excel, follow these steps:

1. Input the Matrix Data:

• Enter your 3×3 matrix into an Excel worksheet. For example, input the following values into cells A1 to C3:
  • A1: -751
  • A2: 2
  • A3: 30
  • B1: -21
  • B2: -56
  • B3: -20
  • C1: 203
  • C2: -2
  • C3: [value from the image]

1. Select the Output Range:

• Highlight a 3×3 range where you want the inverse matrix to appear. For instance, select cells E1 to G3.

1. Enter the MINVERSE Function:

• With the output range selected, type the formula =MINVERSE(A1:C3) into the formula bar.

1. Confirm the Formula:

• If you’re using Excel 365 or Excel 2021, press Enter.
• For earlier versions of Excel, press Ctrl+Shift+Enter to enter the formula as an array formula. Excel will enclose the formula in curly braces {} to indicate it’s an array formula.

1. Review the Results:

• The selected output range (E1:G3) will now display the inverse of your original matrix.

Explanation:

The MINVERSE function in Excel computes the inverse of a given square matrix. The inverse of a matrix is a matrix that, when multiplied by the original matrix, yields the identity matrix. This function is particularly useful in solving systems of linear equations and in various applications of linear algebra.

Important Considerations:

• Matrix Dimensions: Ensure that the matrix is square (i.e., the number of rows equals the number of columns). The MINVERSE function requires a square matrix to compute its inverse.
• Array Formula: In versions of Excel prior to Excel 365, the MINVERSE function must be entered as an array formula. This is done by selecting the output range, typing the formula, and pressing Ctrl+Shift+Enter. In newer versions, pressing Enter is sufficient.
• Error Handling: If the matrix is singular (i.e., it does not have an inverse), the MINVERSE function will return a #NUM! error. A matrix is singular if its determinant is zero, indicating that it cannot be inverted.
• Data Integrity: Ensure that all cells in the matrix contain numerical values. If any cell is empty or contains text, the MINVERSE function will return a #VALUE! error.

By following these steps and considerations, you can effectively compute the inverse of a matrix in Excel, facilitating various mathematical and analytical tasks.