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- Determine two functions, defined on the interval (−∞,∞)(−∞,∞), whose Wronskian is given by W(f1,f2)=e2xW(f1,f2)=e2x. Are the functions that you found linearly independent on (−∞,∞)(−∞,∞)? How do you know?suppose that x,y,z∈R3 are such that x.(y×z)≠0. prove that x,y,z are linearly independent.Find the linearization L(x) at x=a. 
- The linear operator T: R2 --> R2 defined by T (x; y) = (4x + 5y; 2x + y) is it diagonalizable?express ∂w ∂u and ∂w ∂v using the chain rule and by expressing w directly in terms of u and v before differentiating. Then evaluate ∂w ∂u and ∂w ∂v at the point (u,v)=− 2/3 ,2.Find the linearization L(x, y) of f(x, y) = x2 y3 at (a, b) = (2, 1). Use it to estimate f(2.01, 1.02) and f(l.97, 1.01), and compare with values obtained using a calculator.