Multivariate Linear Interpolation

[gifariz]

I am making spreadsheet to interpolate output value from multiple (4 or more) variables. I have found solution for 2 and 3 variables (using bilinear and trilinear interpolation), I need to make for more variables.
Bilinear interpolation:

Trilinear interpolation:


I see some pattern here. I want to expand for more variables linear interpolation using this pattern:
View attachment KakaoTalk_20210318_174353769 (2).jpg

Is it correct?
Thank you in advance.

 

[gifariz]

(I couldn't find the edit button)
There is typo in my handwritten equation, it should be inverse instead of transpose.

And, can I continue this pattern (variable combinations) for 5 or more variables?