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Math Help - An Exercise: Matrix Multiplication

  1. #1
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    Question An Exercise: Matrix Multiplication

    An autoparts manufacturer makes fenders, doors, and hoods. Each requires assembly and packaging carried out at factories: Plant 1, Plant 2, and Plant 3. Matrix A below gives the number of hours for assembly and packaging, and matrix B gives the hourly rates at the three plants. Explain the meaning of the (3,2)-entry in the matrix AB. Which plant is the most economical to operate? Give reasons.

    An Exercise: Matrix Multiplication-untitled.png
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  2. #2
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    \displaystyle AB=C=((c_{jk}))=\sum_{i=1}^{n}a_{ji}b_{ik}
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  3. #3
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    Have you tried multiplying the matrices? What will the rows of \displaystyle \mathbf{AB} represent? What will the columns represent?
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  4. #4
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    Look at the first entry of AB at row 1 column 1:
    12 * 21 + 2 * 14
    = (hours for fender assembly)*(hourly cost of assembly at plant 1) + (hours for fender packaging)*(hourly cost of packaging at plant 1)

    What value does this give?

    Follow this reasoning to see what the (i,j) entry of AB means.
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