MINVERSE

See Also

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

Syntax

MINVERSE(array)

Array is 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, and that these letters 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)

	Column A	Column B
Row 1	d/(ad-bc)	b/(bc-ad)
Row 2	c/(bc-ad)	a/(ad-bc)

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.

Example 1

The example may be easier to understand if you copy it to a blank spreadsheet.

Show How?

Create a blank spreadsheet.
Select the example in the Help topic.

Selecting an example from Help
Press CTRL+C.
In the spreadsheet, select cell A1, and press CTRL+V.
To switch between viewing the formula that returns the result and the result in the cell, select the cell and press F2 and then ENTER, or click Commands and Options on the spreadsheet toolbar, click the Formula tab, and look in the Formula in active cell (active cell) box.

Data	Data
4	-1
2	0
Formula	Formula
=MINVERSE(A2:B3)

Note The formula in the example must be entered as an array formula. After copying the example to a blank spreadsheet, select the range A5:B6 starting with the formula cell. Press F2, and then press CTRL+SHIFT+ENTER. If the formula is not entered as an array formula, the single result is 0.

Example 2

The example may be easier to understand if you copy it to a blank spreadsheet.

Show How?

Create a blank spreadsheet.
Select the example in the Help topic.

Selecting an example from Help
Press CTRL+C.
In the spreadsheet, select cell A1, and press CTRL+V.
To switch between viewing the formula that returns the result and the result in the cell, select the cell and press F2 and then ENTER, or click Commands and Options on the spreadsheet toolbar, click the Formula tab, and look in the Formula in active cell (active cell) box.

Data	Data	Data
1	2	1
3	4	-1
0	2	0
Formula	Formula	Formula
=MINVERSE(A2:C4)

Note The formula in the example must be entered as an array formula. After copying the example to a blank spreadsheet, select the range A6:C8 starting with the formula cell. Press F2, and then press CTRL+SHIFT+ENTER. If the formula is not entered as an array formula, the single result is 0.25.

Show Tip

Use the INDEX function to access individual elements from the inverse matrix.