The Mountain Trail Resort sold 64 condominiums last year, all 1, 2, or 3 bedroom condominiums. The total revenue from the sale of the condominiums was $5,493,000. The combined square footage of all the condominiums sold was 51,544 square feet. One bedroom condominiums sold for $72,000, two bedroom condominiums sold for $87,000, and three bedroom condominiums sold for $102,000. One bedroom condominiums have an area of 512 square feet, two bedroom condominiums have an area of 840 square feet, and three bedroom condominiums have an area of 1120 square feet. How many of each size condominium did Mountain Trail Resort sell last year? Use the matrices A and B below to enter the matrices that you use to solve this problem. Your solution must include a system of equations with a definition of the variables and an explanation of how you solved the problem using matrices.

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[ | | ] =A
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[ | ] =B
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To solve this problem using matrices, we can define the variables and create a system of equations based on the given information.

Let's define:
x = number of one bedroom condominiums sold
y = number of two bedroom condominiums sold
z = number of three bedroom condominiums sold

We can create the following equations based on the given information:

Equation 1: x + y + z = 64 (total number of condominiums sold)

Equation 2: x * 512 + y * 840 + z * 1120 = 51,544 (total square footage)

Equation 3: x * 72,000 + y * 87,000 + z * 102,000 = 5,493,000 (total revenue)

Now, we can represent this system of equations using matrices.

Matrix A:
[1 1 1]
[512 840 1120]
[72,000 87,000 102,000]

Matrix B:
[x]
[y]
[z]

The system of equations can be represented as:
A * B = [64]
[51,544]
[5,493,000]

To solve for B (the vector of variables), we need to find the inverse of A and multiply it with the matrix on the right-hand side.

Matrix B = A^(-1) * [64]
[51,544]
[5,493,000]

By solving this equation, we will get the values for x, y, and z, which represent the number of each size condominium sold last year.

Note: To calculate the inverse of matrix A, if you do not have access to a matrix calculator or software, you can use Gaussian elimination or other methods to find the inverse.

By substituting the values of x, y, and z back into the original equations, you can confirm that the solution is correct.