If `A_(0) = [[2 ,-2,-4],[-1,3,4],[1,-2,-3]] and B_(0) [[-4,-4,-4],[1,0,1],[4,4,3]]` then find` A_0 +B_0`

Explanation

To find the sum of the matrices \( A_0 \) and \( B_0 \), we will follow these steps:

### Step 1: Write down the matrices
The matrices are given as follows:

\[ A_0 = \begin{bmatrix} 2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3 \end{bmatrix} \]

\[ B_0 = \begin{bmatrix} -4 & -4 & -4 \\ 1 & 0 & 1 \\ 4 & 4 & 3 \end{bmatrix} \]

### Step 2: Add the corresponding elements
To find \( A_0 + B_0 \), we will add the corresponding elements from both matrices.

- For the first row:
- First element: \( 2 + (-4) = 2 - 4 = -2 \)
- Second element: \( -2 + (-4) = -2 - 4 = -6 \)
- Third element: \( -4 + (-4) = -4 - 4 = -8 \)

- For the second row:
- First element: \( -1 + 1 = 0 \)
- Second element: \( 3 + 0 = 3 \)
- Third element: \( 4 + 1 = 5 \)

- For the third row:
- First element: \( 1 + 4 = 5 \)
- Second element: \( -2 + 4 = 2 \)
- Third element: \( -3 + 3 = 0 \)

### Step 3: Write the resulting matrix
Combining all the results, we get:

\[ A_0 + B_0 = \begin{bmatrix} -2 & -6 & -8 \\ 0 & 3 & 5 \\ 5 & 2 & 0 \end{bmatrix} \]

### Final Result
Thus, the sum of the matrices \( A_0 + B_0 \) is:

\[ \begin{bmatrix} -2 & -6 & -8 \\ 0 & 3 & 5 \\ 5 & 2 & 0 \end{bmatrix} \]

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