1.

Consider the expressions given below and find if the expressions are symmetric or not (a) `ax + ay + b` (b) `ax^(2) + bxy + ay^(2)`

Answer» (a) Let `f(x, y) = ax + ay + b`
`f(y, x) = ay + ax + b` ltbr `= ax + ay + b`
`rArr f(y,x) = f(x,y)`
`:. ax + ay + b` is symmetric
(b) `f(x,y) = ax^(2) + bxy + ay^(2)`
`f(y, x) = ay^(2) + byx + ax^(2)`
`= ax^(2) + bxy + ay^(2)`
`:. f(y, x) = f(x, y)`
Hence, `ax^(2) + bxy + ay^(2)` is symmetric


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