For an n x n matrix A =
(aij)<ijn over R, define a map (called a quadratic
9: R³ → R
1. Given A, what is the relationship between 44 and 4A+AT? Here AT
denotes the transpose of A.
2. Given A, find a symmetric n x n matrix B such that qa = 9B. 
3. Assume n = 3 and consider the map
-3x+6x1x2 - 4x1x32x² + 4x2x3 + 2x².
Find a symmetric matrix B such that q = qB.