In this lesson:
A store tracks monthly sales for two products across two regions:
This is January. February has a similar table. How would you build a single grid showing two-month totals?
January and February sales: and are both .
Adding each matching position. That move has a name.
The difference recovers January's figures.
Position (1,3) exists in but not in — no partner.
Addition needs identical dimensions — not matching inner dimensions.
Decide: defined or undefined for each pair?
Decide for all four before advancing.
3 shirts × 20 + 5 dresses × 35 = 60 + 175 = 235
That move — multiply corresponding entries, then sum — is the dot product.
Each entry of a matrix product works exactly this way.
In a moment, you'll see how this fills an entire result matrix.
Not entry-wise. You combine an entire row with an entire column.
Row 2 of =
Compute both before advancing.
result
, :
Order always matters — products can have different shapes.
For each product, state result dimensions or "undefined":
State all four before advancing.
,
Student's answer:
What went wrong? Find the correct .
Compute completely with no setup:
Produce all four entries of .
Work the full product before advancing.
:
Manual count of 2-step paths from node 2 to node 3:
Result: 1 path. matches manual count. ✓
If maps Category 1 → Category 2, and maps Category 2 → Category 3:
maps Category 1 → Category 3 directly — no intermediate step needed.
Each entry of combines one row from with one column from : a two-step link compressed into one number.
What does dotting these two lists give you?
✓ Add/subtract — identical dimensions; entry by entry
✓ Multiply — inner dimensions match; each entry = row · column
✓ Result shape —
✓ Order matters — in general
✓ Products encode two-step calculations
VM.C.9 — Non-Commutativity of Matrix Multiplication
You've seen . The next lesson asks:
Click to begin the narrated lesson
Add, subtract, and multiply matrices