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I have a matrix representing the amount of different resources (columns) I would need to create (rows) different objects.

$\begin{bmatrix} 1 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 & 0 \\ 0 & 0 & 2 & 0 & 3 \\ \end{bmatrix}$

My objective is to use matrix multiplication to find out how many resources it would take if we wanted to have i objects of row 1, j objects of row 2, and k objects of row 3.

I don't know an efficient way to go about this. A working solution I have is to split each of the rows and multiply them by scalars i, j, k, but I don't feel as though this is the correct solution.

Is there a way to get the same result by multiplying two matrices? Thank you.

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What you have described is matrix multiplication, and is the correct way to solve the problem.

Let $M$ stand for the $3 \times 5$ resource matrix in the question. Then the $1 \times 5$ matrix $$ [i,j,k]M $$ tells you how many of each of the five kinds of resources you need to manufacture those objects.

The matrix product would look a little more traditional if you wrote the transpose $T$ of the resource consumption matrix instead, where each row corresponds to an ingredient and each column to a kind of object. Then the computation would be the $1 \times 5$ matrix $$ T \begin{bmatrix} i \\ j \\ k \end{bmatrix} $$

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  • $\begingroup$ I'm sorry, can you explain the [i,j,k]A notation? $\endgroup$ – Jersey Fonseca Jan 11 at 22:32
  • $\begingroup$ Multiply the $1\times 3$ matrix $[i,j,k]$ bythe $3 \times 5$ matrix $A$. $\endgroup$ – user3482749 Jan 11 at 22:36

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