Questions: mylabmastering.pearson.com Assignments Create a New Flashcard Set Quizlet mylab.pearson.com Makayla Rodgers 09/20/24 2:49 PM Question 14, 2.4.44 HW Score: 65%, 13 of 20 Part 1 of 3 points Points: 0 of 1 Save Use the following magic multiplication square to answer the following parts (a)-(c). 8 256 2 4 16 64 128 1 32 (a) Verify that the three numbers in every row, column and diagonal in the following square have the same product. The product for each row is □. The product for each column is □. The product along both diagonals is □. Clear all Check answer

Solution Steps

To solve this problem, we need to calculate the product of the numbers in each row, each column, and both diagonals of the given magic multiplication square. We will then verify if these products are the same.

1. Extract the numbers from the given square.
2. Calculate the product of the numbers in each row.
3. Calculate the product of the numbers in each column.
4. Calculate the product of the numbers in both diagonals.
5. Verify if the products are the same for rows, columns, and diagonals.

We are given the following magic multiplication square: \[ \begin{bmatrix} 8 & 256 & 2 \\ 4 & 16 & 64 \\ 128 & 1 & 32 \end{bmatrix} \]

The product for each row is calculated as follows: \[ \begin{aligned} &\text{Row 1: } 8 \times 256 \times 2 = 4096 \\ &\text{Row 2: } 4 \times 16 \times 64 = 4096 \\ &\text{Row 3: } 128 \times 1 \times 32 = 4096 \end{aligned} \]

The product for each column is calculated as follows: \[ \begin{aligned} &\text{Column 1: } 8 \times 4 \times 128 = 4096 \\ &\text{Column 2: } 256 \times 16 \times 1 = 4096 \\ &\text{Column 3: } 2 \times 64 \times 32 = 4096 \end{aligned} \]

The product for both diagonals is calculated as follows: \[ \begin{aligned} &\text{Diagonal 1: } 8 \times 16 \times 32 = 4096 \\ &\text{Diagonal 2: } 2 \times 16 \times 128 = 4096 \end{aligned} \]

We observe that the product for each row, each column, and both diagonals is the same: \[ 4096 \]

Final Answer