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    The matrix s = 5 0 1 6 2
    7 8 4 3 9

    contains the numbers of first and second class stamps ised in my post office each day last week. (Top row denotes fist class).

    1) Find a matrix D such that DS gives the total number of stamps used each day

    2) Find a matrix N such that SN gives the total number of each type of stamp used each week

    3) First class stamps cost 25 pence while second class stamps cost 19 pence. Find a way of calculating the total cost of last weeks stamps using only matrix multiplication.

    Thanks
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    btw the matrix is

    5 0 1 6 2
    7 8 4 3 9

    sorry about the above version!
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    anyone?
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    For question 1, you need to think about the principles of matrix multiplication. How can you get it so that the two numbers in each column are added up? First, think about the order of the matrices that you need to multiply by. You're stuck with an Nx5 matrix, since you've got five columns in the current one, so you need to decide on the number of rows in D. 5 will be needed (for 5 columns in our product matrix) - this is because we want information on 5 different days.

    What matrix can be used to add up the total for each day of the week? Think back to the rules of matrix multiplication: the rows of the first matrix multiply the columns of the second:



    In the above, the first cell of our product matrix is going to be 5a + 7b, the second 0c + 8d, etc..

    Hopefully it's apparent from this that a matrix consisting entirely of 1s should do the trick. Think about it: by multiplying by one, you're not changing any of the numbers, but instead just adding them together:



    A similar principle applies for the next two - remember that matrix multiplication is not commutative, and so pay careful attention to the next question's order!

    Hope this helps - Be sure to post back if you have any problems.
 
 
 
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Updated: October 22, 2006

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