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_O`

Explanation

To find \( A_0 - B_0 \), we will perform matrix subtraction. Let's break down the process step by step.

### Step 1: Write down the matrices \( A_0 \) and \( B_0 \).

Given:
\[ A_0 = \begin{bmatrix} 2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3 \end{bmatrix} \]
\[ B_0 = \begin{bmatrix} -4 & -4 & -4 \\ 1 & 0 & 1 \\ 4 & 4 & 3 \end{bmatrix} \]

### Step 2: Set up the subtraction \( A_0 - B_0 \).

We will subtract each corresponding element of \( B_0 \) from \( A_0 \):
\[ A_0 - B_0 = \begin{bmatrix} 2 - (-4) & -2 - (-4) & -4 - (-4) \\ -1 - 1 & 3 - 0 & 4 - 1 \\ 1 - 4 & -2 - 4 & -3 - 3 \end{bmatrix} \]

### Step 3: Calculate each element of the resulting matrix.

1. For the first row:
- \( 2 - (-4) = 2 + 4 = 6 \)
- \( -2 - (-4) = -2 + 4 = 2 \)
- \( -4 - (-4) = -4 + 4 = 0 \)

2. For the second row:
- \( -1 - 1 = -2 \)
- \( 3 - 0 = 3 \)
- \( 4 - 1 = 3 \)

3. For the third row:
- \( 1 - 4 = -3 \)
- \( -2 - 4 = -6 \)
- \( -3 - 3 = -6 \)

### Step 4: Combine the results into the final matrix.

Putting all the calculated elements together, we get:
\[ A_0 - B_0 = \begin{bmatrix} 6 & 2 & 0 \\ -2 & 3 & 3 \\ -3 & -6 & -6 \end{bmatrix} \]

### Final Answer:
\[ A_0 - B_0 = \begin{bmatrix} 6 & 2 & 0 \\ -2 & 3 & 3 \\ -3 & -6 & -6 \end{bmatrix} \]

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