Returns the inverse matrix for the matrix stored in an array.
Syntax
MINVERSE(array)
Argument | Description | Remarks |
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array | A numeric array with an equal number of rows and columns. | -
The
array argument can be given as a cell range, such as A1:C3; as an
array constantA set of data used to build single formulas that produce multiple results or that operate on a group of arguments arranged in rows and columns. Excel
has two kinds of arrays: array ranges and array constants. An array range is a rectangular area of cells that share a common formula; an array constant is a specially arranged group of constants that's used as an argument in a formula., such as {1,2,3;4,5,6;7,8,9}; or as a name for either of these.
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If any cells in
array are empty or contain text, this function returns the #VALUE! error value.
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This function returns the #VALUE! error value if
array does not have an equal number of rows and columns.
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Formulas that return arrays must be entered as array formulas.
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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.
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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.
 | | 1 | | 2 |
| | A | B | | d/(a*d-b*c) | b/(b*c-a*d) | | c/(b*c-a*d) | a/(a*d-b*c) |
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MINVERSE is calculated with an accuracy of approximately 16 digits, which may lead to a small numeric error when the calculation is not complete.
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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: Returning Inverse matrix for the matrix stored in a two-column array |
To make the following example easier to understand, you can copy the data to a blank sheet and then enter the function underneath the data. Do not select the row or column headings (1, 2, 3... A, B, C...) when you copy the sample data to a blank sheet.
 | Note The formula in the example must be entered as an array formula. First, type the formula into cell A5 and then press
RETURN. The single result is 0. Next, select the range A5:B6, press
CONTROL+U, and then press
⌘+RETURN. The array results, from left to right and top to bottom, are 0, 0.5, -1, and 2. |
| | 1 | | 2 | | 3 |
| | A | B | | Data | Data | | 4 | -1 | | 2 | 0 | | Formula | | | =MINVERSE(A2:B3) | | | | |
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| Example 2: Returning Inverse matrix for the matrix stored in a three-column array |
To make the following example easier to understand, you can copy the data to a blank sheet and then enter the function underneath the data. Do not select the row or column headings (1, 2, 3... A, B, C...) when you copy the sample data to a blank sheet.
| Note The formula in the example must be entered as an array formula. First, type the formula into cell A6 and then press
RETURN. The single result is 0.25. Next, select the range A6:C8, press
CONTROL+U, and then press
⌘+RETURN. The array results, from left to right and top to bottom, are 0.25, 0.25, -0.75, 0, 0, 0.5, 0.75, -0.25, and -0.25. |
| | 1 | | 2 | | 3 | | 4 |
| | A | B | C | | Data | Data | Data | | 1 | 2 | 1 | | 3 | 4 | -1 | | 0 | 2 | 0 | | Formula | | | | =MINVERSE(A2:C4) | | | | | | | | | | |
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