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?

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.

Tags: excelexcel