The MINVERSE function in Google Sheets is a powerful tool for users working with mathematical concepts, particularly in linear algebra. It computes the multiplicative inverse of a square matrix, enabling complex calculations in various applications such as engineering, finance, and data analysis.

Syntax

MINVERSE(array)

• array: A range or array representing a square matrix that you want to find the inverse for. The matrix must have an equal number of rows and columns.

Example #1

MINVERSE({1, 2; 3, 4})

This function calculates the inverse of the 2×2 matrix {{1, 2}, {3, 4}}. The result is {{-2, 1}, {1.5, -0.5}}.

Example #2

MINVERSE(A1:B2)

Assuming cells A1 through B2 contain the values {{2, 3}, {5, 7}}, this function will compute the inverse of that matrix, yielding {{-7, 3}, {5, -2}}.

Example #3

MINVERSE(D1:F3)

If D1 through F3 forms a 3×3 square matrix, this function will return its inverse. For instance, if the matrix is {{1, 0, 2}, {0, 1, 3}, {0, 0, 1}}, the output will be the corresponding inverse matrix for that input.

Error handling

• REF! This error occurs if the specified array is not a valid square matrix (i.e., the number of rows does not equal the number of columns).
• VALUE! This appears when the input is not a valid range or array.
• NUM! This error is returned if the matrix is singular (i.e., it does not have an inverse).

Conclusion

In summary, the MINVERSE function is an essential tool for anyone working with square matrices in Google Sheets. By enabling users to calculate the multiplicative inverse of matrices, it opens up numerous possibilities for data manipulation and analysis. Understanding the syntax and potential errors associated with this function can enhance your spreadsheet skills and lead to more sophisticated data handling.