Does the sum `[(5,3,2),(2,5,3),(5,2,3)]+[(0,0,0),(0,0,0)]` make sense ?
If so, find the sum and if not, give the reason.

Answer

To determine whether the sum of the matrices \(\begin{pmatrix} 5 & 3 & 2 \\ 2 & 5 & 3 \\ 5 & 2 & 3 \end{pmatrix}\) and \(\begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix}\) makes sense, we need to check the dimensions of both matrices.

### Step 1: Identify the dimensions of the matrices
- The first matrix, let's call it \( A \), is given by:
\[ A = \begin{pmatrix} 5 & 3 & 2 \\ 2 & 5 & 3 \\ 5 & 2 & 3 \end{pmatrix} \]
This matrix has 3 rows and 3 columns, so its order is \( 3 \times 3 \).

- The second matrix, let's call it \( B \), is given by:
\[ B = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} \]
This matrix has 2 rows and 3 columns, so its order is \( 2 \times 3 \).

### Step 2: Compare the dimensions for addition
For two matrices to be added, they must have the same dimensions. This means:
- The number of rows in matrix \( A \) must equal the number of rows in matrix \( B \).
- The number of columns in matrix \( A \) must equal the number of columns in matrix \( B \).

In this case:
- Matrix \( A \) has 3 rows and 3 columns.
- Matrix \( B \) has 2 rows and 3 columns.

### Step 3: Conclusion
Since the number of rows in matrix \( A \) (which is 3) is not equal to the number of rows in matrix \( B \) (which is 2), the addition of these matrices is **not possible**.

### Final Answer
The sum \(\begin{pmatrix} 5 & 3 & 2 \\ 2 & 5 & 3 \\ 5 & 2 & 3 \end{pmatrix} + \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix}\) does not make sense because the dimensions of the matrices are not the same.

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