If `X+{:[(2,1),(6,1)]:}={:[(1,1),(0,1)]:}` then 'X' is equal to

Options

A. `{:[(0,1),(0,6)]:}`
B. `{:[(0,-1),(0,-6)]:}`
C. `{:[(-1,0),(-6,0)]:}`
D. `{:[(1,0),(6,0)]:}`

Answer

To solve the equation \( X + \begin{pmatrix} 2 & 1 \\ 6 & 1 \end{pmatrix} = \begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix} \), we will isolate \( X \) by subtracting the matrix on the left from both sides.

### Step-by-Step Solution:

1. **Write down the equation:**
\[ X + \begin{pmatrix} 2 & 1 \\ 6 & 1 \end{pmatrix} = \begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix} \]

2. **Subtract the matrix \( \begin{pmatrix} 2 & 1 \\ 6 & 1 \end{pmatrix} \) from both sides:**
\[ X = \begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix} - \begin{pmatrix} 2 & 1 \\ 6 & 1 \end{pmatrix} \]

3. **Perform the matrix subtraction element-wise:**
- For the element at (1,1): \( 1 - 2 = -1 \)
- For the element at (1,2): \( 1 - 1 = 0 \)
- For the element at (2,1): \( 0 - 6 = -6 \)
- For the element at (2,2): \( 1 - 1 = 0 \)

Thus, we have:
\[ X = \begin{pmatrix} -1 & 0 \\ -6 & 0 \end{pmatrix} \]

4. **Final result:**
\[ X = \begin{pmatrix} -1 & 0 \\ -6 & 0 \end{pmatrix} \]

### Conclusion:
The value of \( X \) is \( \begin{pmatrix} -1 & 0 \\ -6 & 0 \end{pmatrix} \).