Chapter 3.6, Problem 8E

To determine

To find: The property illustrated in part b of Activity 2.

Answer to Problem 8E

Associative property of Matrix addition

Explanation of Solution

Given information: $A=\left[\begin{array}{cc}-6& 2\\ 7& 3\end{array}\right],B=\left[\begin{array}{cc}5& 1\\ -8& 4\end{array}\right],C=\left[\begin{array}{cc}11& -3\\ 4& -1\end{array}\right]$

  $(A+B)+C$ and $A+(B+C)$ are both equal to $\left[\begin{array}{cc}10& 0\\ 3& 6\end{array}\right]$

Calculation:

In part b of Activity 2 it is observed,

  $(A+B)+C=A+(B+C)=\left[\begin{array}{cc}10& 0\\ 3& 6\end{array}\right]$

So, the addition of 3 matrices gives the same result irrespective of the order of grouping of the matrices A, B and C.

The Associative property of matrix addition states that, for any three matrices A, B and C , of same dimensions, $(A+B)+C=A+(B+C)$ .

Hence, Associative property of matrix addition is illustrated in part b of Activity 2.