# Problem 3 of 3

A store in Kenora, Ontario sells items that are tax free, items that have a 7% GST charge on the base price, and items that have both a 7% GST and an 8% PST charge on the base price. A weekend's sales, before tax, can be represented by Matrix S.

(a) What does the matrix represent?

(b) What does the matrix represent?

(c) What does the matrix (*S* + 0.07*A* + 0.08*B*) represent?

(d) Write a matrix to represent the total tax collected. Briefly explain how you constructed this matrix.

(e) New budgets change the tax rates to 5% for GST and 12% for PST. Write a matrix for the total taxes collected in this new situation. Briefly explain how you contructed this matrix.

**Solution**

(a) Matrix A represents the items that were sold on a weekend's sale, that had been taxed.

(b) Matrix B represents items sold with both GST and PST.

(c) (*S* + 0.07*A* + 0.08*B*) represents the total of items sold including taxes.

(d)

I constructed the resultant matrix that represented the total tax collected by multiplying 0.07 to matrix A, then I added that to a scalar multipication of matrix B multiplied by 0.08. 0.07 represents the GST tax and 0.08 represented the PST tax for each matrix.

(e) New tax rates to 5% for GST and 12% for PST.

I constructed the resultant matrix with the new tax rates changes by taking matrix A and multiplying it by the new GST which is 5%, then I added it to matrix B which was multiplied by the new PST which is 12%. With the resultant matrix I got the new total of taxes collected with the new tax rate changes.

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