Question

How would i set this matrix up?

Answer 1

Step-by-step explanation:

The first column of matrix P must correspond to the first row of matrix I.

So if the first column in P is number of cherry pies, the first row in I must be the cost of cherry pie ingredients.

Fortunately, the table is already set up in the correct order.  So all you have to do is write it as a matrix.

$P = \left[\begin{array}{cccc}3&4&1&1\\6&6&4&6\\2&2&5&4\end{array}\right]$

$I = \left[\begin{array}{cccc}3\\5\\2\\6\end{array}\right]$

To multiply the matrices, start with the first row of matrix P.

3 4 1 1

Multiply each value by the corresponding row of matrix I.

3×3 = 9, 4×5 = 20, 1×2 = 2, 1×6 = 6

Add the results.

9 + 20 + 2 + 6 = 37

This is the value in the first row and first column of matrix PI.  If matrix I had another column, we would add another column to PI and repeat this step for the new column.  Since matrix I has only one column, we're finished with this row of PI.

Here's the result:

$PI = \left[\begin{array}{cccc}3\times3+4\times5+1\times2+1\times6\\6\times3+6\times5+4\times2+6\times6\\2\times3+2\times5+5\times2+4\times6\end{array}\right] \\PI = \left[\begin{array}{cccc}9+20+2+6\\18+30+8+36\\6+10+10+24\end{array}\right]\\PI = \left[\begin{array}{cccc}37\\92\\50\end{array}\right]$