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Database System Concepts
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
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(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) ```
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 ```
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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