Practice question · Multiple choice
A retailer cannot add its 3×4 sales matrix to its 4×3 cost matrix, even though both hold twelve numbers. Why does the rule refuse?
Hints
- Ask what entry (2,3) means in each matrix.
- The shapes differ. What would you be adding to what?
Show the answer
A. Because addition is entrywise and each entry means something specific
Why
Position carries the meaning in a matrix, so same-shape is the requirement that entry (i,j) refers to the same thing in both. It is the same discipline as not adding kilometres to kilograms, the arithmetic would run and the answer would be nonsense.
Practise Matrix Addition
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