Chapter 2, Problem 36E

To determine

To create:

• A $3\times 5$ matrix, and find the maximum value in each column.

• A $3\times 5$ matrix, and find the maximum value in each row.

• A $3\times 5$ matrix, and find the maximum value in the entire matrix.

• A $3\times 5$ matrix, and find the cumulative maxima.

Answer to Problem 36E

Solution:

• A $3\times 5$ matrix is $\text{mat}=\left[\begin{array}{ccccc}5& 3& -10& -8& -4\\ 5& -7& -5& 7& 9\\ -2& 4& -10& 4& -10\end{array}\right]$. And the maximum value in each column is 5, 4, -5, 7, and 9 respectively.

• A $3\times 5$ matrix is $\text{mat}=\left[\begin{array}{ccccc}-4& -3& -9& 9& -1\\ 5& 1& 1& -8& -10\\ 5& -9& 6& 1& -3\end{array}\right]$. And the maximum value in each row is 9, 5, and 6 respectively.

• A $3\times 5$ matrix is $\text{mat}=\left[\begin{array}{ccccc}-7& 1& -5& 5& -6\\ 6& -7& 3& -1& 9\\ -4& 2& 4& -9& -7\end{array}\right]$. And the maximum value in the entire matrix is 9.

• A $3\times 5$ matrix is $\text{mat}=\left[\begin{array}{ccccc}-1& -5& 8& -7& -3\\ 9& -7& 2& 7& 0\\ -7& -8& 1& 3& -2\end{array}\right]$. And the cumulative maxima are 9, 4, -6, 3 and 12 respectively.

Explanation of Solution

• A $3\times 5$ matrix, and find the maximum value in each column.

MATLAB Code:

clc

clear all

close all

mat = randi([-10, 10], 3, 5)

% Define the command to generate a random numbers.

max(mat)

% Define the command to find the maximum value in each column.

Save the MATLAB script with name, chapter2_54793_2_39_1E.m in the current folder. Execute the script by typing the script name at the command window to create a $3\times 5$ matrix. And find the maximum value in each column.

Result:

Therefore, a $3\times 5$ matrix is $\text{mat}=\left[\begin{array}{ccccc}5& 3& -10& -8& -4\\ 5& -7& -5& 7& 9\\ -2& 4& -10& 4& -10\end{array}\right]$. And the maximum value in each column is 5, 4, -5, 7, and 9 respectively.

• A $3\times 5$ matrix, and find the maximum value in each row.

MATLAB Code:

clc

clear all

close all

mat = randi([-10, 10], 3, 5)

% Define the command to generate a random numbers.

max(mat')

% Define the command to find the maximum value in each row.

Save the MATLAB script with name, chapter2_54793_2_39_2E.m in the current folder. Execute the script by typing the script name at the command window to create a $3\times 5$ matrix. And find the maximum value in each row.

Result:

Therefore, a $3\times 5$ matrix is $\text{mat}=\left[\begin{array}{ccccc}-4& -3& -9& 9& -1\\ 5& 1& 1& -8& -10\\ 5& -9& 6& 1& -3\end{array}\right]$. And the maximum value in each row is 9, 5, and 6 respectively.

• A $3\times 5$ matrix, and find the maximum value in the entire matrix.

MATLAB Code:

clc

clear all

close all

mat = randi([-10, 10], 3, 5)

% Define the command to generate a random numbers.

max(max(mat))

% Define the command to find the maximum value in the entire matrix.

Save the MATLAB script with name, chapter2_54793_2_39_3E.m in the current folder. Execute the script by typing the script name at the command window to create a $3\times 5$ matrix. And find the maximum value in the entire matrix.

Result:

Therefore, a $3\times 5$ matrix is $\text{mat}=\left[\begin{array}{ccccc}-7& 1& -5& 5& -6\\ 6& -7& 3& -1& 9\\ -4& 2& 4& -9& -7\end{array}\right]$. And the maximum value in the entire matrix is 9.

• A $3\times 5$ matrix, and find the cumulative maxima.

MATLAB Code:

clc

clear all

close all

mat = randi([-10, 10], 3, 5)

% Define the command to generate a random numbers.

cumsum(mat)

% Define the command to create the cumulative matrix variable.

max(cumsum(vec))

% Define the command to select the smallest value.

Save the MATLAB script with name, chapter2_54793_2_39_4E.m in the current folder. Execute the script by typing the script name at the command window to create a $3\times 5$ matrix. And find the maximum value in the entire matrix.

Result:

Therefore, a $3\times 5$ matrix is $\text{mat}=\left[\begin{array}{ccccc}-1& -5& 8& -7& -3\\ 9& -7& 2& 7& 0\\ -7& -8& 1& 3& -2\end{array}\right]$. And the cumulative maxima are 9, 4, -6, 3 and 12 respectively.