Chapter C, Problem C.27E

a.

To determine

By using MATLAB to find $A+B+C$.

Answer to Problem C.27E

$A+B+C=\left(\begin{array}{cc}-4& 2\\ 22& 15\end{array}\right)$.

Explanation of Solution

Given Information:

$A=\left(\begin{array}{cc}-7& 16\\ 4& 9\end{array}\right)$.

$B=\left(\begin{array}{cc}6& -5\\ 12& -2\end{array}\right)$.

$C=\left(\begin{array}{cc}-3& -9\\ 6& 8\end{array}\right)$.

MATLAB commands:

A = [-7 16;4 9]

B = [6 -5;12 -2]

C = [-3 -9;6 8]

A + B + C

MATLAB window below

Conclusion:

$A+B+C=\left(\begin{array}{cc}-4& 2\\ 22& 15\end{array}\right)$.

b.

To determine

By using MATLAB to find $A-B+C$.

Answer to Problem C.27E

$A-B+C=\left(\begin{array}{cc}-16& 12\\ -2& 19\end{array}\right)$.

Explanation of Solution

Given Information:

$A=\left(\begin{array}{cc}-7& 16\\ 4& 9\end{array}\right)$.

$B=\left(\begin{array}{cc}6& -5\\ 12& -2\end{array}\right)$.

$C=\left(\begin{array}{cc}-3& -9\\ 6& 8\end{array}\right)$.

MATLAB commands:

A = [-7 16;4 9]

B = [6 -5;12 -2]

C = [-3 -9;6 8]

A - B + C

MATLAB window below

Conclusion:

$A-B+C=\left(\begin{array}{cc}-16& 12\\ -2& 19\end{array}\right)$.

c.

To determine

By using MATLAB to verify the associative law $(A+B)+C=A+(B+C)$.

Answer to Problem C.27E

$(A+B)+C=\left(\begin{array}{cc}-4& 2\\ 22& 15\end{array}\right)$.

$A+(B+C)=\left(\begin{array}{cc}-4& 2\\ 22& 15\end{array}\right)$.

Hence, $(A+B)+C=A+(B+C)$.

Explanation of Solution

Given Information:

$A=\left(\begin{array}{cc}-7& 16\\ 4& 9\end{array}\right)$.

$B=\left(\begin{array}{cc}6& -5\\ 12& -2\end{array}\right)$.

$C=\left(\begin{array}{cc}-3& -9\\ 6& 8\end{array}\right)$.

MATLAB commands:

A = [-7 16;4 9]

B = [6 -5;12 -2]

C = [-3 -9;6 8]

(A + B)+ C

A + (B + C)

MATLAB window below

Conclusion:

$(A+B)+C=\left(\begin{array}{cc}-4& 2\\ 22& 15\end{array}\right)$.

$A+(B+C)=\left(\begin{array}{cc}-4& 2\\ 22& 15\end{array}\right)$.

Hence, $(A+B)+C=A+(B+C)$.

d.

To determine

By using MATLAB to verify the commutative law $A+B+C=A+C+B=B+C+A$.

Answer to Problem C.27E

$A+B+C=\left(\begin{array}{cc}-4& 2\\ 22& 15\end{array}\right)$.

$A+C+B=\left(\begin{array}{cc}-4& 2\\ 22& 15\end{array}\right)$.

$B+C+A=\left(\begin{array}{cc}-4& 2\\ 22& 15\end{array}\right)$.

Hence, $A+B+C=A+C+B=B+C+A$.

Explanation of Solution

Given Information:

$A=\left(\begin{array}{cc}-7& 16\\ 4& 9\end{array}\right)$.

$B=\left(\begin{array}{cc}6& -5\\ 12& -2\end{array}\right)$.

$C=\left(\begin{array}{cc}-3& -9\\ 6& 8\end{array}\right)$.

MATLAB commands:

A = [-7 16;4 9]

B = [6 -5;12 -2]

C = [-3 -9;6 8]

A + B + C

A + C + B

B + C + A

MATLAB window below

Conclusion:

$A+B+C=\left(\begin{array}{cc}-4& 2\\ 22& 15\end{array}\right)$.

$A+C+B=\left(\begin{array}{cc}-4& 2\\ 22& 15\end{array}\right)$.

$B+C+A=\left(\begin{array}{cc}-4& 2\\ 22& 15\end{array}\right)$.

Hence, $A+B+C=A+C+B=B+C+A$.