15. Advanced problem: Let's say that a vector space Xsplits the spaces U and G if either U X & W or W X V. a. Is there a vector space C that splits A = R^3 and B = {the x-axis in R^3} ? If there is, find it (no need to prove your claim) and if not, explain why it cannot exist. b. Suppose that U & W are a finite-dimensional. On what condition does there exist a vector space that splits them? (no need to prove your claim) c. Is there a vector space F that splits D = span{sinx -cosx, 3sinx_2cosx, 2sinx-cosx} and E = span{sinx, cosx, e^x, e^-x}? If so, find it (no need to prove your claim) and if not, explain why it cannot exist