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# MINVERSE function

This article describes the formula syntax and usage of the MINVERSE function in Microsoft Excel.

## Description

Returns the inverse matrix for the matrix stored in an array.

## Syntax

MINVERSE(array)

The MINVERSE function syntax has the following arguments:

• Array    Required. A numeric array with an equal number of rows and columns.

## Remarks

• Array can be given as a cell range, such as A1:C3; as an array constant, such as {1,2,3;4,5,6;7,8,9}; or as a name for either of these.

• If any cells in Array are empty or contain text, MINVERSE returns the #VALUE! error value.

• MINVERSE also returns the #VALUE! error value if array does not have an equal number of rows and columns.

• Formulas that return arrays must be entered as array formulas.

• Inverse matrices, like determinants, are generally used for solving systems of mathematical equations involving several variables. The product of a matrix and its inverse is the identity matrix — the square array in which the diagonal values equal 1, and all other values equal 0.

• As an example of how a two-row, two-column matrix is calculated, suppose that the range A1:B2 contains the letters a, b, c, and d that represent any four numbers. The following table shows the inverse of the matrix A1:B2.

 Column A Column B Row 1 d/(a*d-b*c) b/(b*c-a*d) Row 2 c/(b*c-a*d) a/(a*d-b*c)
• MINVERSE is calculated with an accuracy of approximately 16 digits, which may lead to a small numeric error when the cancellation is not complete.

• Some square matrices cannot be inverted and will return the #NUM! error value with MINVERSE. The determinant for a noninvertable matrix is 0.

## Examples

### Example 1

Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.

 Data 4 -1 2 0 Formula Description Results =MINVERSE(A2:B3) Note: To work correctly, the formula needs to be entered as an array formula in the Excel program.After copying the example to a blank worksheet, select the range C5:D6 starting with the formula cell. Press F2, and then press Ctrl+Shift+Enter. If the formula is not entered as an array formula, a single result (0) is returned in C5. 0 0.5 -1 2

### Example 2

Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.

 Data 1 2 1 3 4 -1 0 2 0 Formula Desciption Results =MINVERSE(A2:C4) To work correctly, the formula needs to be entered as an array formula in the Excel program.After copying the example to a blank worksheet, select the range C6:E8 starting with the formula cell. Press F2, and then press Ctrl+Shift+Enter. If the formula is not entered as an array formula, a single result (0.25) is displayed in C6. 0.25 0.25 -0.75 0 0 0.5 0.75 -0.25 -0.25

Applies To: Excel 2016, Excel 2010, Excel Starter, Excel 2013, Excel Online, Excel 2016 for Mac, Excel for Mac 2011, Excel 2007

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