BitWithBite
AI & Machine Learning Worksheet
🤖 Matrix Operations
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Matrix multiply rulesTransposeIdentity and inverseShapes must align📚 Quick Recap
Matrix multiplication is not what most people guess on first encounter (multiplying each matching position together, like you would with two vectors). It's a different, specific operation, and getting the rule straight now will save you from a very common bug later: shape mismatch errors, which are probably the single most common error message you'll see across every lab in this entire course track.
🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1(2x3) times (3x4) gives shape:
2Transpose swaps:
3A x I =:
4A matrix has an inverse only if det is:
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5To multiply AB, A's columns must equal B's .
6(A^T)^T = .
7Can you multiply (3x2)(3x2)? Why?
8Compute [[1,2],[3,4]] x [[1,0],[0,1]].
9Where does W x + b appear in ML?
🚀 Section C · Challenge ● CHALLENGE 5
10Transpose of [[1,2,3],[4,5,6]]?
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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✂ answer key — fold or cut before handing out
1-A 2-A 3-A 4-A | 5 rows 6 A 7 = No - inner dims 2 and 3 differ; transpose one first 8 = Same matrix (identity property) 9 = Every linear/dense layer of a network | 10 = [[1,4],[2,5],[3,6]] - shape (3,2)