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- Compute the Wronskian for 2t^2y''+3ty'-y=0Show that the image of the annulus {1<|z|<2} under w=2/(z-1) is the domain {W: Re(W)>-1, |W=2/3|>4/3} using Möbius transformation.a. Show that W[5, sin2 t, cos(2t)] = 0 for all t by directly evaluating the Wrosnkian. b. Establish the same result without direct evaluation of the Wronskian.
- Let L : R 2 → R 3 be defined by L(x, y) = (x − y, 0, x + y). Show that L is a linear transformation. What is the kernel of L? What is the nullity of and rank of L?. Let Dn be as in Example 10. Find a Hamiltonian circuit inCay({(r, 0), (f, 0), (e, 1)}:D4 ⨁ Z5).Does your circuit generalize to the case Dn ⨁ Zn+1 for all n ≥ 4?Show that Z/mnZ is isomphoric to (Z/mZ)×(Z/nZ) where gcd(m,n) = 1
- Show that A and AT have the same nonzero singular values. How are their singular value decompositions related?If the Wronskian of f and g is tcost-sint, and if u=f+2g, v=f-g, find the Wronskian of u and v.The main point of this exercise is to use Green’s Theorem to deduce a specialcase of the change of variable formula. Let U, V ⊆ R2 be path connected open sets and letG : U → V be one-to-one and C2such that the derivate DG(u) is invertible for all u ∈ U.Let T ⊆ U be a regular region with piecewise smooth boundary, and let S = G(T). Solve all of them plz