Chapter 6.6, Problem 36HP

To determine

To explain: whether $3\times 2$ matrix and a $2\times 3$ matrix can be added

Answer to Problem 36HP

Matrices $A$ and $B$ cannot be added

Explanation of Solution

Calculation:

To add two matrices, add corresponding components of the matrices.

Thus to add two matrices, the order of the matrices must be same.

Therefore, no, it is not possible to add a $3\times 2$ matrix and a $2\times 3$ matrix.

Let $A=\left[\begin{array}{lll}1\hfill & 0\hfill & 1\hfill \\ 1\hfill & 0\hfill & 0\hfill \end{array}\right]$ and $B=\left[\begin{array}{ll}0\hfill & 1\hfill \\ 1\hfill & 0\hfill \\ 1\hfill & 0\hfill \end{array}\right]$

Then $A$ is a $3\times 2$ matrix and $B$ is a $2\times 3$ matrix. So, matrices $A$ and $B$ cannot be added

Conclusion:

Then $A$ is a $3\times 2$ matrix and $B$ is a $2\times 3$ matrix. So, matrices $A$ and $B$ cannot be added