The numbers of three types of bank accounts on January 1 at the Central Bank and its branches are represented by matrix A. Fixed- deposit accounts 1120 Main office A = Westside branch 1030 Eastside branch 1190 The number and types of accounts opened during the first quarter are represented by matrix B, and the number and types of accounts closed during the same period are represented by matrix C. Thus, 260 120 110 120 80 80 140 60 50 70 30 40 120 70 50 60 40 (a) Find matrix D, which represents the number of each type of account at the end of the first quarter at each location. E ↓ 1 B = D= Checking Savings accounts accounts 2840 1470 520 540 E = and C = (b) Because a new manufacturing plant is opening in the immediate area, it is anticipated that there will be a 10% increase in the number of accounts at each location during the second quarter. Write a matrix E = 1.1D to reflect this anticipated increase. 688 460 480 J
The numbers of three types of bank accounts on January 1 at the Central Bank and its branches are represented by matrix A. Fixed- deposit accounts 1120 Main office A = Westside branch 1030 Eastside branch 1190 The number and types of accounts opened during the first quarter are represented by matrix B, and the number and types of accounts closed during the same period are represented by matrix C. Thus, 260 120 110 120 80 80 140 60 50 70 30 40 120 70 50 60 40 (a) Find matrix D, which represents the number of each type of account at the end of the first quarter at each location. E ↓ 1 B = D= Checking Savings accounts accounts 2840 1470 520 540 E = and C = (b) Because a new manufacturing plant is opening in the immediate area, it is anticipated that there will be a 10% increase in the number of accounts at each location during the second quarter. Write a matrix E = 1.1D to reflect this anticipated increase. 688 460 480 J
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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![The numbers of three types of bank accounts on January 1 at the Central Bank and its branches are represented by matrix A.
Matrix A:
- Main office:
- Checking accounts: 2840
- Savings accounts: 1470
- Fixed-deposit accounts: 1120
- Westside branch:
- Checking accounts: 1030
- Savings accounts: 520
- Fixed-deposit accounts: 460
- Eastside branch:
- Checking accounts: 1190
- Savings accounts: 540
- Fixed-deposit accounts: 480
The number and types of accounts opened during the first quarter are represented by matrix B, and the number and types of accounts closed during the same period are represented by matrix C. Thus,
Matrix B:
\[
B = \begin{bmatrix}
260 & 120 & 110 \\
140 & 60 & 50 \\
120 & 70 & 50
\end{bmatrix}
\]
Matrix C:
\[
C = \begin{bmatrix}
120 & 80 & 70 \\
30 & 40 & 60 \\
20 & 40 & 40
\end{bmatrix}
\]
(a) Find matrix D, which represents the number of each type of account at the end of the first quarter at each location.
Matrix D:
\[
D = \begin{bmatrix}
\quad & \quad & \quad \\
\quad & \quad & \quad \\
\quad & \quad & \quad
\end{bmatrix}
\]
(Arrows indicate the calculation process to fill in Matrix D.)
(b) Because a new manufacturing plant is opening in the immediate area, it is anticipated that there will be a 10% increase in the number of accounts at each location during the second quarter. Write a matrix E = 1.1D to reflect this anticipated increase.
Matrix E:
\[
E = \begin{bmatrix}
\quad & \quad & \quad \\
\quad & \quad & \quad \\
\quad & \quad & \quad
\end{bmatrix}
\]
(The empty boxes are placeholders to be filled with the calculated values.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79cbc358-f9c7-4513-8a58-8a5e6560b01b%2F74637ed6-5662-4932-8b71-a3ed39c1ac99%2Fzibxfz7_processed.png&w=3840&q=75)
Transcribed Image Text:The numbers of three types of bank accounts on January 1 at the Central Bank and its branches are represented by matrix A.
Matrix A:
- Main office:
- Checking accounts: 2840
- Savings accounts: 1470
- Fixed-deposit accounts: 1120
- Westside branch:
- Checking accounts: 1030
- Savings accounts: 520
- Fixed-deposit accounts: 460
- Eastside branch:
- Checking accounts: 1190
- Savings accounts: 540
- Fixed-deposit accounts: 480
The number and types of accounts opened during the first quarter are represented by matrix B, and the number and types of accounts closed during the same period are represented by matrix C. Thus,
Matrix B:
\[
B = \begin{bmatrix}
260 & 120 & 110 \\
140 & 60 & 50 \\
120 & 70 & 50
\end{bmatrix}
\]
Matrix C:
\[
C = \begin{bmatrix}
120 & 80 & 70 \\
30 & 40 & 60 \\
20 & 40 & 40
\end{bmatrix}
\]
(a) Find matrix D, which represents the number of each type of account at the end of the first quarter at each location.
Matrix D:
\[
D = \begin{bmatrix}
\quad & \quad & \quad \\
\quad & \quad & \quad \\
\quad & \quad & \quad
\end{bmatrix}
\]
(Arrows indicate the calculation process to fill in Matrix D.)
(b) Because a new manufacturing plant is opening in the immediate area, it is anticipated that there will be a 10% increase in the number of accounts at each location during the second quarter. Write a matrix E = 1.1D to reflect this anticipated increase.
Matrix E:
\[
E = \begin{bmatrix}
\quad & \quad & \quad \\
\quad & \quad & \quad \\
\quad & \quad & \quad
\end{bmatrix}
\]
(The empty boxes are placeholders to be filled with the calculated values.)
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