Matrix Inverse and Multiplication

Matrix inverse and multiplication in Excel is an excellent way to simultaneously solve multivariate equations. There are, however, a few restrictions.

First, it must be a square matrix (n x n). Here’s the photo from which I decided to calculation this matrix:

Second, where coefficients do not exist, you must enter a 0.

Third, it helps if you properly label your workspace.

Given the set of equations in the photo, this is how things should look before performing the matrix operations:

The requisite steps are simple:

1Check that it’s a square matrix (n x n):  (A2:D5)
2Highlight (select) an equal-sized (n x n) blank space:  (A8:D11)
3Type:  =minverse(array), and for “array” highlight the x1 through xn array (A2:D5), above.
4Hit CTRL-SHIFT-ENTER
5Highlight (select) a 1 x n blank space (to the right of x1, x2, x3, x4):  (G8:G11)
6Type:  =mmult(array 1, array 2), where array1 is the n x n inverse (A8:D11) and array2 is the y (1 x n) matrix: (F2:F5)
7Hit CTRL-SHIFT-ENTER
8Observe the resulting solution for X1, X2, X3 and X4

Here’s the matrix, the inverse and the multiplied result:

The primary limit is that arrays using the MINVERSE function cannot exceed 52 rows by 52 columns. Not only did Lotus 123 not have this problem, but it took only three steps to invert a matrix and multiply it against the y products.

Updated: October 12, 2020 — 2:16 pm