Let T is a linear transformation. Find the standard matrix of T such that 1. T:R^2 → R^4 by T(e1) = (3, 1, 3, 1) and T(e 2) = ( 5, 2, 0, 0) where e 1 = (1, 0) and e 2 = (0, 1); 1. T:R^2 → R^4…

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

1. T:R^2 → R^4 by T(e1) = (3, 1, 3, 1) and T(e_2) = (-5, 2, 0, 0) where e_1 = (1, 0) and e_2 = (0, 1);
2. T:R^2 → R^4 rotates point as the origin through $\frac{3\pi }{4}$ radians counter clockwise.
3. T:R^2 → R^4 Is a vertical shear transformation that maps e_1 into e_1-2e_2 but leaves vector e_2 unchanged.