mathlab code
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Related questions
Question
make mathlab code
![(Matrix-Vector Multiplication) The product of a matrix \( A \) and a (column) vector \( \vec{x} \) is defined provided the number of columns of \( A \) is equal to the number of rows of \( \vec{x} \). Suppose this is the case, and let \( A \) be \( m \times n \) and \( \vec{x} \) be \( n \times 1 \). Then, the product \( A\vec{x} \) is defined element-wise by
\[
(A\vec{x})_j = \sum_{k=1}^{n} A_{j,k}x_k.
\]
For this problem, do not use the built-in ability to multiply matrices and vectors.
**mat_vec Function:**
- **Input variables:**
- a matrix representing \( A \)
- a vector representing \( \vec{x} \)
- **Output variables:**
- a vector representing \( A\vec{x} \); if the sizes do not match, return an empty vector (produced by [] in MATLAB)
A possible sample case is:
```
>> b = mat_vec([1 2 ; 2 1], [2 ; -2])
b =
-2
2
b = mat_vec([1 2 ; 3 4], [5])
b = [](0x0)
```](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93507587-8486-4bd1-9be9-7c1c5dc70b2a%2Fd667746b-ad56-44d1-87fe-454a32d3ff8f%2Ft9wslbg_processed.png&w=3840&q=75)
Transcribed Image Text:(Matrix-Vector Multiplication) The product of a matrix \( A \) and a (column) vector \( \vec{x} \) is defined provided the number of columns of \( A \) is equal to the number of rows of \( \vec{x} \). Suppose this is the case, and let \( A \) be \( m \times n \) and \( \vec{x} \) be \( n \times 1 \). Then, the product \( A\vec{x} \) is defined element-wise by
\[
(A\vec{x})_j = \sum_{k=1}^{n} A_{j,k}x_k.
\]
For this problem, do not use the built-in ability to multiply matrices and vectors.
**mat_vec Function:**
- **Input variables:**
- a matrix representing \( A \)
- a vector representing \( \vec{x} \)
- **Output variables:**
- a vector representing \( A\vec{x} \); if the sizes do not match, return an empty vector (produced by [] in MATLAB)
A possible sample case is:
```
>> b = mat_vec([1 2 ; 2 1], [2 ; -2])
b =
-2
2
b = mat_vec([1 2 ; 3 4], [5])
b = [](0x0)
```
![(Minimum and Maximum) We often want to find the minimum and maximum values in a vector as well as the indices at which these values occur.
For this problem **do not** use the built-in `min` or `max` function (or any other function which trivializes the problem).
**min_max Function:**
- **Input variables:**
- a vector representing the list of numbers; you may assume each value is unique
- **Output variables:**
- a scalar representing the minimum value
- a scalar representing the index where the minimum value is located in the list
- a scalar representing the maximum value
- a scalar representing the index where the maximum value is located in the list
A possible sample case is:
```
>> [min_val, min_i, max_val, max_i] = min_max(1:5)
min_val = 1
min_i = 1
max_val = 5
max_i = 5
>> [min_val, min_i, max_val, max_i] = min_max([2, 3, 7, 1, 4])
min_val = 1
min_i = 4
max_val = 7
max_i = 3
>> [min_val, min_i, max_val, max_i] = LXX_QYY([1, 2, 3, 4, -1, 0])
min_val = -1
min_i = 5
max_val = 4
max_i = 4
```](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93507587-8486-4bd1-9be9-7c1c5dc70b2a%2Fd667746b-ad56-44d1-87fe-454a32d3ff8f%2Fgwnld37_processed.png&w=3840&q=75)
Transcribed Image Text:(Minimum and Maximum) We often want to find the minimum and maximum values in a vector as well as the indices at which these values occur.
For this problem **do not** use the built-in `min` or `max` function (or any other function which trivializes the problem).
**min_max Function:**
- **Input variables:**
- a vector representing the list of numbers; you may assume each value is unique
- **Output variables:**
- a scalar representing the minimum value
- a scalar representing the index where the minimum value is located in the list
- a scalar representing the maximum value
- a scalar representing the index where the maximum value is located in the list
A possible sample case is:
```
>> [min_val, min_i, max_val, max_i] = min_max(1:5)
min_val = 1
min_i = 1
max_val = 5
max_i = 5
>> [min_val, min_i, max_val, max_i] = min_max([2, 3, 7, 1, 4])
min_val = 1
min_i = 4
max_val = 7
max_i = 3
>> [min_val, min_i, max_val, max_i] = LXX_QYY([1, 2, 3, 4, -1, 0])
min_val = -1
min_i = 5
max_val = 4
max_i = 4
```
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