How can I solve a system of linear equations in Excel

Question

I am having some trouble finding a solution for a system of equations using excel.
The system is of the form Ax=b, with A a matrix and x and b vectors. Obviously, the goal is to find x.

The system does not necessarily have the same number of equations and unknowns. An exact solution is not always possible. Therefor I want to find the best approximation, possibly using least squares.

Are there standard methods in Excel to do that?
If not, can someone provide me with a macro that does that or explain how I can write my own?

Thanks

Answer 1

Check the LINEST() function.

Answer 2

You can use the pseudoinverse and Excel's matrix functions. Suppose there is a named range _A containing your matrix, and another named range _b containing your vector, then you can select an appropriately shaped set of cells and enter the formula:

=MMULT((MINVERSE(MMULT(TRANSPOSE(_A); _A))); MMULT(TRANSPOSE(_A); _b))

Remember to press Control-Shift-Enter to enter this formula as it is an array formula. It will appear with braces around it when you select the cells.