# Matrix Multiplication Application

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.

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 $$T \begin{bmatrix} i \\ j \\ k \end{bmatrix}$$
• Multiply the $1\times 3$ matrix $[i,j,k]$ bythe $3 \times 5$ matrix $A$. – user3482749 Jan 11 at 22:36