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

1. T:R² → R⁴ by T(e1) = (3, 1, 3, 1) and T(e₂) = (-5, 2, 0, 0) where e₁ = (1, 0) and e₂ = (0, 1);
2. T:R² → R⁴ rotates point as the origin through \(\frac{3\pi}{4}\) radians counter clockwise.
3. T:R² → R⁴ Is a vertical shear transformation that maps e₁ into e₁-2e₂ but leaves vector e₂ unchanged.