Solved using python.

 

Assume that (x, y, z) are nx 1 column vectors and {A, B, C} are n x n real-valued matrices, O is the zero matrix of appropriate size, and I is the identity matrix of appropriate size. State whether each of the below is true in general (you do not need to show your work). 1. xy = Xi Yi- 2. xx= |x||- xx. 3. xx 4. (x - y)(y-x) = ||x|| -2xy + ||||- 5. AB = BA. 6. A(B+C) = AB + AC 7. (AB) = ATBT. 8. x Ay=yAx. 9. ATA I if the columns of A are orthonormal. UC