For a symmetric matrix, the element at position (row i, column j) equals the element at position (row j, column i).
Given matrix:
A=−12y624−13x−10
Position (1,2) = 2
Position (2,1) = 2y
Position (1,3) = 3x
Position (3,1) = 6
Since the matrix is symmetric, the mirror positions must be equal.
Comparing position (1,2) with position (2,1):
2=2y
y=1
Comparing position (1,3) with position (3,1):
3x=6
x=2
The value of 2x−y:
2x−y=2(2)−1
2x−y=4−1
2x−y=3
Therefore, the value of 2x−y is 3.