Manjeet wants to donate a rectangular plot of land for a school in his village. When he has asked to give dimensions of the plot, he told that if its length is decreased by 50 m and breadth is increased by 50 m, then its area will remain same, but if its length is decreased by 10 m and breadth is decreased by 20 m, then its area will decrease by 5300 m². If length and breadth of the plot are x and y respectively, then based on above information answer the question.

The linear equation involving x and y are written in matrix form as:

\(\begin{bmatrix}1 & -1 \\2 & 1 \end{bmatrix}\)\(\begin{bmatrix}x  \\y \end{bmatrix}\)=\(\begin{bmatrix}50\\500 \end{bmatrix}\)

$x-y=50 ....(i)$

$2x+y=550 ....(ii)$

From eq. (i) & (ii)

\(A=\begin{bmatrix}1 & -1 \\2 & 1 \end{bmatrix}\)\(X=\begin{bmatrix}x  \\y \end{bmatrix}\)=\(B=\begin{bmatrix}50\\500 \end{bmatrix}\)

\(\begin{bmatrix}1 & -1 \\2 & 1 \end{bmatrix}\)\(\begin{bmatrix}x  \\y \end{bmatrix}\)=\(\begin{bmatrix}50\\500 \end{bmatrix}\)

Option A is correct.