If `A={:[(1,2),(-1,8),(4,9)]:}andX+A=0`, then X is equal to

Options

A. `{:[(1,2),(1,8),(4,9)]:}`
B. `{:[(-1,-2),(1,8),(4,9)]:}`
C. `{:[(1,2),(1,-8),(4,9)]:}`
D. `{:[(-1,-2),(1,-8),(-4,-9)]:}`

Answer

To solve the problem step by step, we start with the given information:

1. We have a matrix \( A \) defined as:
\[ A = \begin{pmatrix} 1 & 2 \\ -1 & 8 \\ 4 & 9 \end{pmatrix} \]

2. The equation we need to solve is:
\[ X + A = 0 \]

3. To isolate \( X \), we can rearrange the equation:
\[ X = -A \]

4. Now, we will substitute the value of \( A \) into the equation:
\[ X = -\begin{pmatrix} 1 & 2 \\ -1 & 8 \\ 4 & 9 \end{pmatrix} \]

5. Next, we will apply the negative sign to each element of the matrix \( A \):
\[ X = \begin{pmatrix} -1 & -2 \\ -(-1) & -8 \\ -4 & -9 \end{pmatrix} \]

6. Simplifying the elements, we get:
\[ X = \begin{pmatrix} -1 & -2 \\ 1 & -8 \\ -4 & -9 \end{pmatrix} \]

Thus, the value of \( X \) is:
\[ X = \begin{pmatrix} -1 & -2 \\ 1 & -8 \\ -4 & -9 \end{pmatrix} \]