For engineers who already know the math—but still lose projects. For the last few years, I’ve been sharing technical guides here on Mechanical Design Handbook —how to size a motor, how to calculate fits, and (as you recently read) how to choose between timing belts and ball screws. But after 25 years in industrial automation, I realized something uncomfortable: Projects rarely fail because the math was wrong. They fail because: The client changed the scope three times in one week. A critical vendor lied about a shipping date (and no one verified it). The installation technician couldn’t fit a wrench into the gap we designed. University taught us the physics. It didn’t teach us the reality. That gap is why I wrote my new book, The Sheet Mechanic . This is not a textbook. It is a field manual for the messy, political, and chaotic space between the CAD model and the factory floor. It captures the systems I’ve used to survive industrial projec...
Figure 1: Visualizing dynamic matrix scaling for large engineering systems.
Scaling Up: Handling N x N Systems
In Part 4, we looked at the basic user interface. But engineering problems aren't fixed at 3x3. A truss analysis might need 10 equations; a thermal grid might need 100.
A professional Excel tool must be Dynamic. It should automatically resize the input table based on the user's needs, clearing old data and preparing fresh cells for input.
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1. User Input for Dimensions
The process starts with a simple input request. In our design, clicking "Main Menu" > "New Equations" triggers a VBA InputBox or UserForm asking for the number of variables (N).
Figure 2: The user selects "New Equations" from the main menu.
For this example, let's input 10 to simulate a larger structural problem.
Figure 3: Specifying a 10-variable system.
2. Managing Data Integrity
When resizing a matrix, you must decide what to do with old data. Our reference design includes a safety check: "Existing equations will be deleted." This prevents users from mixing data from a 3x3 problem with a new 10x10 grid.
Figure 4: A safety warning prevents accidental data loss.
3. Automating the Resize (VBA Logic)
Behind the scenes, your VBA code needs to do the heavy lifting.
How it works conceptually:
- Clear Range: The code identifies the old range (e.g., B3:D5) and runs
.ClearContents. - Redefine Range: Based on the input N=10, the code calculates the new range (B3:K12).
- Formatting: It applies borders and background colors to the new range so the user knows exactly where to type.
Figure 5: The spreadsheet automatically formats a clean 10x10 input grid.
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4. Solving the Large System
Once the data is entered, the Gauss Elimination algorithm we wrote in Part 1 handles the 10x10 matrix just as easily as the 3x3.
Figure 6: Inputting coefficients for a larger system.
Clicking "Solve" populates the 10x1 result vector instantly.
Figure 7: The algorithm computes the 10 unknowns instantly.
5. Verification: The MMULT Function
Trust but verify. A good engineer always checks the results. In Excel, you can use the built-in function =MMULT() to multiply your original [A] matrix by the calculated {X} vector.
If the result matches your original {B} vector, the solution is correct.
Figure 8: Using
MMULT to multiply [A]*{X} confirms the solution matches {B}.Conclusion
By combining robust math (Gauss Elimination) with smart VBA (Dynamic Ranges), you can build powerful engineering tools that rival commercial software.
In the final post, we will share a video demonstration of this tool in action.
Continue to Part 6:
Solving System of Equations using Gauss Elimination Method (Part 6: Video Demo)
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