Laura is planning to buy three 5-lb bags of sugar, six 5-lb bags of flour, three 1-gal cartons of milk, and six 1-dozen cartons of large eggs. The prices of these items in three neighborhood supermarkets are as follows. A = B = Supermarket I Supermarket II Supermarket III (a) Write a 3 x 4 matrix A to represent the prices (in dollars) of the items in the three supermarkets. 11 C= Sugar (5-lb bag) $3.15 $2.99 $3.74 ↓1 (b) Write a 4 x 1 matrix B to represent the quantities of sugar, flour, milk, and eggs that Laura plans to purchase in the three supermarkets. 11 Flour (5-lb bag) $3.79 $2.89 $2.98 49 Milk (1-gal carton) $2.99 $2.79 $2.89 Eggs (1-dozen carton) $3.49 $3.29 $2.99 (c) Use matrix multiplication to find a matrix C that represents Laura's total outlay (in dollars) at each supermarket.
Laura is planning to buy three 5-lb bags of sugar, six 5-lb bags of flour, three 1-gal cartons of milk, and six 1-dozen cartons of large eggs. The prices of these items in three neighborhood supermarkets are as follows. A = B = Supermarket I Supermarket II Supermarket III (a) Write a 3 x 4 matrix A to represent the prices (in dollars) of the items in the three supermarkets. 11 C= Sugar (5-lb bag) $3.15 $2.99 $3.74 ↓1 (b) Write a 4 x 1 matrix B to represent the quantities of sugar, flour, milk, and eggs that Laura plans to purchase in the three supermarkets. 11 Flour (5-lb bag) $3.79 $2.89 $2.98 49 Milk (1-gal carton) $2.99 $2.79 $2.89 Eggs (1-dozen carton) $3.49 $3.29 $2.99 (c) Use matrix multiplication to find a matrix C that represents Laura's total outlay (in dollars) at each supermarket.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Matrix Representation of Prices and Quantities**
Laura is planning to buy three 5-lb bags of sugar, six 5-lb bags of flour, three 1-gal cartons of milk, and six 1-dozen cartons of large eggs. The prices of these items in three neighborhood supermarkets are as follows:
| | Sugar (5-lb bag) | Flour (5-lb bag) | Milk (1-gal carton) | Eggs (1-dozen carton) |
|-----------------|------------------|------------------|---------------------|-----------------------|
| **Supermarket I** | $3.15 | $3.79 | $2.99 | $3.49 |
| **Supermarket II**| $2.99 | $2.89 | $2.79 | $3.29 |
| **Supermarket III**| $3.74 | $2.98 | $2.89 | $2.99 |
1. **(a) Write a 3 x 4 matrix A to represent the prices (in dollars) of the items in the three supermarkets.**
\[
A = \begin{pmatrix}
3.15 & 3.79 & 2.99 & 3.49 \\
2.99 & 2.89 & 2.79 & 3.29 \\
3.74 & 2.98 & 2.89 & 2.99 \\
\end{pmatrix}
\]
2. **(b) Write a 4 x 1 matrix B to represent the quantities of sugar, flour, milk, and eggs that Laura plans to purchase in the three supermarkets.**
\[
B = \begin{pmatrix}
3 \\
6 \\
3 \\
6 \\
\end{pmatrix}
\]
3. **(c) Use matrix multiplication to find a matrix C that represents Laura's total outlay (in dollars) at each supermarket.**
Matrix multiplication between A and B:
\[
C = AB = \begin{pmatrix}
3.15 & 3.79 & 2.99 & 3.49 \\
2.99 & 2.89 & 2.79 &](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77247d15-844d-4e77-b205-212be8c6419e%2Fd880b789-9227-447d-be95-07b804ded628%2Fr3dkmok_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Matrix Representation of Prices and Quantities**
Laura is planning to buy three 5-lb bags of sugar, six 5-lb bags of flour, three 1-gal cartons of milk, and six 1-dozen cartons of large eggs. The prices of these items in three neighborhood supermarkets are as follows:
| | Sugar (5-lb bag) | Flour (5-lb bag) | Milk (1-gal carton) | Eggs (1-dozen carton) |
|-----------------|------------------|------------------|---------------------|-----------------------|
| **Supermarket I** | $3.15 | $3.79 | $2.99 | $3.49 |
| **Supermarket II**| $2.99 | $2.89 | $2.79 | $3.29 |
| **Supermarket III**| $3.74 | $2.98 | $2.89 | $2.99 |
1. **(a) Write a 3 x 4 matrix A to represent the prices (in dollars) of the items in the three supermarkets.**
\[
A = \begin{pmatrix}
3.15 & 3.79 & 2.99 & 3.49 \\
2.99 & 2.89 & 2.79 & 3.29 \\
3.74 & 2.98 & 2.89 & 2.99 \\
\end{pmatrix}
\]
2. **(b) Write a 4 x 1 matrix B to represent the quantities of sugar, flour, milk, and eggs that Laura plans to purchase in the three supermarkets.**
\[
B = \begin{pmatrix}
3 \\
6 \\
3 \\
6 \\
\end{pmatrix}
\]
3. **(c) Use matrix multiplication to find a matrix C that represents Laura's total outlay (in dollars) at each supermarket.**
Matrix multiplication between A and B:
\[
C = AB = \begin{pmatrix}
3.15 & 3.79 & 2.99 & 3.49 \\
2.99 & 2.89 & 2.79 &
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