Rows/columns/order and labelled contextual matrices; Addition/subtraction/scalar multiplication; Matrix products and summing with unit row/column vectors; Technology and costing/inventory applications; model usefulness
Example 1
Orders are row vector [3,4] and prices are column vector [10,5]ᵀ dollars. Find total cost.
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Answer: 50
Multiply corresponding quantities and prices, then add the products.
Example 2
A=[[5,2],[2,2]] and B=[[1,2],[3,4]]. Find the top-right entry of AB.
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Answer: 18
Take the dot product of the first row of A and second column of B.
Example 3
A has order 2×3 and B has order 3×4. What is the order of AB?
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Answer: 2×4
The matching inner dimension is 3; the result uses the outer dimensions 2 and 4.
Put it into practice.
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