Find matrix A, if `[(1,2,-1),(0,4,9)]+A=[(9,-1,4),(-2,1,3)]`

Options

A. `[(8,-3,-5),(-2,-3,-6)]`
B. `[(8,-3,5),(-2,-3,-6)]`
C. `[(8,-3,5),(2,-3,6)]`
D. None of these

Answer

To find the matrix \( A \), we start with the equation:

\[ [(1, 2, -1), (0, 4, 9)] + A = [(9, -1, 4), (-2, 1, 3)] \]

### Step 1: Isolate Matrix A
To isolate matrix \( A \), we can subtract the matrix on the left from both sides of the equation:

\[ A = [(9, -1, 4), (-2, 1, 3)] - [(1, 2, -1), (0, 4, 9)] \]

### Step 2: Perform Element-wise Subtraction
Now we will perform the subtraction element-wise.

For the first row:
- First element: \( 9 - 1 = 8 \)
- Second element: \( -1 - 2 = -3 \)
- Third element: \( 4 - (-1) = 4 + 1 = 5 \)

For the second row:
- First element: \( -2 - 0 = -2 \)
- Second element: \( 1 - 4 = -3 \)
- Third element: \( 3 - 9 = -6 \)

### Step 3: Combine the Results
Now we can combine the results from both rows to form matrix \( A \):

\[ A = [(8, -3, 5), (-2, -3, -6)] \]

### Final Answer
Thus, the matrix \( A \) is:

\[ A = \begin{pmatrix} 8 & -3 & 5 \\ -2 & -3 & -6 \end{pmatrix} \]

---