Chapter 15, Problem 19P

(a)

To determine

Find the addition of matrix $\left[A\right]\text{and}\left[B\right]$ using MATLAB.

Explanation of Solution

Given data:

The matrices $\left[A\right]$, $\left[B\right]$, and $\left[C\right]$ are,

$\left[A\right]=\left[\begin{array}{ccc}4& 2& 1\\ 7& 0& -7\\ 1& -5& 3\end{array}\right]$

$\left[B\right]=\left[\begin{array}{ccc}1& 2& -1\\ 5& 3& 3\\ 4& 5& -7\end{array}\right]$

$\left[C\right]=\left[\begin{array}{c}1\\ -2\\ 4\end{array}\right]$

Calculation:

The steps to add the matrix $\left[A\right]\text{and}\left[B\right]$ using MATLAB are as follows:

• Input the matrix $\left[A\right]\text{and}\left[B\right]$.
• Using the code “$\left[A\right]+\left[B\right]$” add the matrix.
• Print the addition of matrix $\left[A\right]\text{and}\left[B\right]$.

In the command window of the MATLAB type the code as follows:

A=[4 2 1;7 0 -7;1 -5 3];

B=[1 2 -1;5 3 3;4 5 -7];

C=[1;-2;4];

add=A+B;

disp(add);

The output will be displayed as follows:

     5     4     0

    12     3    -4

     5     0    -4

Conclusion:

Thus, the addition of matrix $\left[A\right]\text{and}\left[B\right]$ is performed using MATLAB.

(b)

To determine

Find the subtraction of matrix $\left[A\right]\text{and}\left[B\right]$ using MATLAB.

Explanation of Solution

Given data:

The matrices $\left[A\right]$, $\left[B\right]$, and $\left[C\right]$ are,

$A=\left[\begin{array}{ccc}4& 2& 1\\ 7& 0& -7\\ 1& -5& 3\end{array}\right]$

$B=\left[\begin{array}{ccc}1& 2& -1\\ 5& 3& 3\\ 4& 5& -7\end{array}\right]$

$C=\left[\begin{array}{c}1\\ -2\\ 4\end{array}\right]$

Calculation:

The steps to subtract the matrix $\left[A\right]\text{and}\left[B\right]$ using MATLAB are as follows:

• Input the matrix $\left[A\right]\text{and}\left[B\right]$.
• Using the code “$\left[A\right]-\left[B\right]$” sub the matrix.
• Print the subtraction of matrix $\left[A\right]\text{and}\left[B\right]$.

In the command window of the MATLAB type the code as follows:

A=[4 2 1;7 0 -7;1 -5 3];

B=[1 2 -1;5 3 3;4 5 -7];

C=[1;-2;4];

sub=A-B;

disp(sub);

The output will be displayed as follows:

     3     0     2

     2    -3   -10

    -3   -10    10

Conclusion:

Thus, the subtraction of matrix $\left[A\right]\text{and}\left[B\right]$ is performed using MATLAB.

(c)

To determine

Find the value of $3\left[A\right]$ using MATLAB.

Explanation of Solution

Given data:

The matrices $\left[A\right]$, $\left[B\right]$, and $\left[C\right]$ are,

$A=\left[\begin{array}{ccc}4& 2& 1\\ 7& 0& -7\\ 1& -5& 3\end{array}\right]$

$B=\left[\begin{array}{ccc}1& 2& -1\\ 5& 3& 3\\ 4& 5& -7\end{array}\right]$

$C=\left[\begin{array}{c}1\\ -2\\ 4\end{array}\right]$

Calculation:

The steps to find the 3 times of matrix $\left[A\right]$ using MATLAB are as follows:

• Input the matrix $\left[A\right]$.
• Using the code “$3*\left[A\right]$” find the value of 3 times the matrix.
• Print the 3 times of matrix $\left[A\right]$.

In the command window of the MATLAB type the code as follows:

A=[4 2 1;7 0 -7;1 -5 3];

X=3*A;

% where X is the resultant matrix.

disp(X);

The output will be displayed as follows:

    12     6     3

    21     0   -21

     3   -15     9

Conclusion:

Thus, the value of $3\left[A\right]$ is performed using MATLAB.

(d)

To determine

Find the multiplication of matrix $\left[A\right]\text{and}\left[B\right]$ using MATLAB.

Explanation of Solution

Given data:

The matrices $\left[A\right]$, $\left[B\right]$, and $\left[C\right]$ are,

$A=\left[\begin{array}{ccc}4& 2& 1\\ 7& 0& -7\\ 1& -5& 3\end{array}\right]$

$B=\left[\begin{array}{ccc}1& 2& -1\\ 5& 3& 3\\ 4& 5& -7\end{array}\right]$

$C=\left[\begin{array}{c}1\\ -2\\ 4\end{array}\right]$

Calculation:

The steps to multiply the matrix $A\text{and}B$ using MATLAB are as follows:

• Input the matrix $\left[A\right]\text{and}\left[B\right]$.
• Using the code “$\left[A\right]*\left[B\right]$” multiply the matrix.
• Print the multiplication of matrix $\left[A\right]\text{and}\left[B\right]$.

In the command window of the MATLAB type the code as follows:

A=[4 2 1;7 0 -7;1 -5 3];

B=[1 2 -1;5 3 3;4 5 -7];

C=[1;-2;4];

Mul=A*B;

disp(Mul);

The output will be displayed as follows:

    18    19    -5

   -21   -21    42

   -12     2   -37

Conclusion:

Therefore, the multiplication of matrix $\left[A\right]\text{and}\left[B\right]$ is performed using MATLAB.

(e)

To determine

Find the multiplication of matrix $\left[A\right]\text{and}\left[C\right]$ using MATLAB.

Explanation of Solution

Given data:

The matrices $\left[A\right]$, $\left[B\right]$, and $\left[C\right]$ are,

$A=\left[\begin{array}{ccc}4& 2& 1\\ 7& 0& -7\\ 1& -5& 3\end{array}\right]$

$B=\left[\begin{array}{ccc}1& 2& -1\\ 5& 3& 3\\ 4& 5& -7\end{array}\right]$

$C=\left[\begin{array}{c}1\\ -2\\ 4\end{array}\right]$

Calculation:

The steps to multiply the matrix $\left[A\right]\text{and}\left[C\right]$ using MATLAB are as follows:

• Input the matrix $\left[A\right]\text{and}\left[C\right]$.
• Using the code “$\left[A\right]*\left[C\right]$” multiply the matrix.
• Print the multiplication of matrix $\left[A\right]\text{and}\left[C\right]$.

In the command window of the MATLAB type the code as follows:

A=[4 2 1;7 0 -7;1 -5 3];

B=[1 2 -1;5 3 3;4 5 -7];

C=[1;-2;4];

Mul=A*C;

disp(Mul);

The output will be displayed as follows:

     4

   -21

    23

Conclusion:

Therefore, the multiplication of matrix $\left[A\right]\text{and}\left[C\right]$ is performed using MATLAB.