Chapter 2, Problem 41E

To determine

To create:

The variables for these two matrices and perform these operations “A+B”, “A-B” and “A.B”.

Answer to Problem 41E

Solution:

The variables for the given two matrices are “A = [1:1:3; 4 -1 6]”, and “B = [2 4 1; -1 3 0]” and the output of these operations “A+B”, “A-B”, and “A.B” are $\left[\begin{array}{ccc}3& 6& 4\\ 5& 2& 6\end{array}\right]$, $\left[\begin{array}{ccc}-1& -2& 2\\ 3& -4& 6\end{array}\right]$, and “Error using” respectively.

Explanation of Solution

The given matrices are,

$\text{A}=\left[\begin{array}{ccc}1& 2& 3\\ 4& -1& 6\end{array}\right]$

And,

$\text{B}=\left[\begin{array}{ccc}2& 4& 1\\ 1& 3& 0\end{array}\right]$

Substitute $\left[\begin{array}{ccc}1& 2& 3\\ 4& -1& 6\end{array}\right]$ for A and $\left[\begin{array}{ccc}2& 4& 1\\ 1& 3& 0\end{array}\right]$ for B in the expression “A+B”.

$\begin{array}{rll}\text{A}+\text{B}& =& \left[\begin{array}{ccc}1& 2& 3\\ 4& -1& 6\end{array}\right]+\left[\begin{array}{ccc}2& 4& 1\\ 1& 3& 0\end{array}\right]\\ & =& \left[\begin{array}{ccc}1+2& 2+4& 3+1\\ 4+1& -1+3& 6+0\end{array}\right]\\ & =& \left[\begin{array}{ccc}3& 6& 4\\ 5& 2& 6\end{array}\right]\end{array}$

Therefore, the elements of the matrix “A+B” are $\left[\begin{array}{ccc}3& 6& 4\\ 5& 2& 6\end{array}\right]$.

Substitute $\left[\begin{array}{ccc}1& 2& 3\\ 4& -1& 6\end{array}\right]$ for A and $\left[\begin{array}{ccc}2& 4& 1\\ 1& 3& 0\end{array}\right]$ for B in the expression “A-B”.

$\begin{array}{rll}\text{A}-\text{B}& =& \left[\begin{array}{ccc}1& 2& 3\\ 4& -1& 6\end{array}\right]-\left[\begin{array}{ccc}2& 4& 1\\ 1& 3& 0\end{array}\right]\\ & =& \left[\begin{array}{ccc}1-2& 2-4& 3-1\\ 4-1& -1-3& 6-0\end{array}\right]\\ & =& \left[\begin{array}{ccc}-1& -2& 2\\ 3& -4& 6\end{array}\right]\end{array}$

Therefore, the elements of the matrix “A-B” are $\left[\begin{array}{ccc}-1& -2& 2\\ 3& -4& 6\end{array}\right]$.

Substitute $\left[\begin{array}{ccc}1& 2& 3\\ 4& -1& 6\end{array}\right]$ for A and $\left[\begin{array}{ccc}2& 4& 1\\ 1& 3& 0\end{array}\right]$ for B in the expression “A*B”.

$\text{A*B}=\left[\begin{array}{ccc}1& 2& 3\\ 4& -1& 6\end{array}\right]\left[\begin{array}{ccc}2& 4& 1\\ 1& 3& 0\end{array}\right]$

The multiplication of the matrix is not possible.

Now, verify the expression output through the MATLAB command.

MATLAB Code:

A = [1:1:3; 4 -1 6]

% Define the command to get the matrix “A”.

B = [2 4 1; -1 3 0]

% Define the command to get the matrix “B”.

A+B

% Define the command to get the output of the expression “A+B”.

A-B

% Define the command to get the output of the expression “A-B”.

A.*B

% Define the command to get the output of the expression “A.*B” (values of matrix A is multiplied with all the elements of matrix B).

Save the MATLAB script with name, chapter2_54793_2_41E.m in the current folder. Execute the script by typing the script name at the command window to create the variables for given two matrices and perform the following operations “A+B”, “A-B” and “A.B”.

Result:

Therefore, the variables for the given two matrices are “A = [1:1:3; 4 -1 6]”, and “B = [2 4 1; -1 3 0]” and the output of these operations “A+B”, “A-B”, and “A.B” are $\left[\begin{array}{ccc}3& 6& 4\\ 5& 2& 6\end{array}\right]$, $\left[\begin{array}{ccc}-1& -2& 2\\ 3& -4& 6\end{array}\right]$, and “Error using” respectively.