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excel – MMULT / MINVERSE Maximum array size

Posted by: admin May 14, 2020 Leave a comment

Questions:

I am attempting to solve this set of equations:

696x +  405y +  61z    = 1385699
618x +  463y +  81z    = 1401476
573x +  476y +  113z   = 1407438
508x +  537y +  117z   = 1418256
473x +  566y +  123z   = 1427224

x,y and z are removed in the worksheet.

Using the following formula: E2:E5 {=MMULT(MINVERSE("A1:C5"),"D1:D5")}

But I keep encountering value errors.

Can MINVERSE only be used with a 3×3 matrix?

How to&Answers:

Since your system of equations is overdetermined you may instead be looking to find the pseudoinverse or least squares estimate. To calculate this, select a 1 x 3 range such as F1:H1 then enter the array formula:

=LINEST(D1:D5,A1:C5,0)

entered by holding down CTRL+SHIFT+ENTER. For the given example, this returns {z,y,x} = {1191.8,1345.3,1103.7}. Note that the results coincide with MINVERSE for square matrices.