A symmetric matrix has the property that the element at position (i,j) equals the element at position (j,i).
The given matrix is:
34−52a03−5b10
Comparing position (1,2) with position (2,1):
Position (1,2) = 2a
Position (2,1) = 4
For symmetry:
2a=4
a=2
Comparing position (2,3) with position (3,2):
Position (2,3) = b
Position (3,2) = 3
For symmetry:
b=3
Computing 5a+2b:
5a+2b=5(2)+2(3)
=10+6
=16
Therefore, the value of 5a+2b is 16.