Mathematics II - Old Questions

4. Let T is a linear transformation. Find the standard matrix of T such that

(i) by T(e1) = (3, 1, 3, 1) and T(e₂) = (-5, 2, 0, 0) where e₁ = (1, 0) and e₂ = (0, 1); 

(ii) rotates point as the origin through radians counter clockwise.

(iii) Is a vertical shear transformation that maps e₁ into e₁-2e₂ but leaves vector e₂ unchanged.