Step-by-step Solution:

Concept:

Two matrices may be added or subtracted only if they have the same dimension; that is, they must have the same number of rows and columns. 

Addition or subtraction is accomplished by adding or subtracting corresponding elements.

 

Calculations:

Given, \(A=\begin{bmatrix} -1 & 2 \\ 3 & 4 \end{bmatrix} \ \text{and} \; \rm B = \ \begin{bmatrix} 3 & -2 \\ 1 & 5 \end{bmatrix} \)

Consider, 2A + B + X = 0

⇒ \( \rm 2\begin{bmatrix} -1 & 2 \\ 3 & 4 \end{bmatrix} + \ \begin{bmatrix} 3 & -2 \\ 1 & 5 \end{bmatrix} + X = \begin{bmatrix} 0 & 0\\ 0 &0 \end{bmatrix}\)

Two matrices may be added or subtracted only if they have the same dimension; that is, they must have the same number of rows and columns. Addition or subtraction is accomplished by adding or subtracting corresponding elements.

⇒ \( \rm \begin{bmatrix} 1 & 2 \\ 7 & 13 \end{bmatrix} + X = \begin{bmatrix} 0 & 0\\ 0 & 0 \end{bmatrix}\)

⇒ X = \( \begin{bmatrix} 0 & 0\\ 0 &0 \end{bmatrix} \) - \( \rm \begin{bmatrix} 1 & 2 \\ 7 & 13 \end{bmatrix} \)

⇒ X = \( \rm \begin{bmatrix} -1 & -2 \\ - 7 & -13 \end{bmatrix} \)