- 2 1 Show That All Solutions Of A Linear Homogeneous And Nth Order Ordina Differential Equation Constitute An N Dimensi 1 (10.18 KiB) Viewed 37 times
- 2 1 Show That All Solutions Of A Linear Homogeneous And Nth Order Ordina Differential Equation Constitute An N Dimensi 2 (44.93 KiB) Viewed 37 times
2.5. The linear vector space formed by all real-valued functions which are contin- uous on the interval -1<x< 1 is denoted by C[ - 1,1). Which of the following subsets of C[ - 1,1) are subspaces: (i) The set of all differentiable functions; (ii) the set of all polynomials of degree n; (iii) the set of all even functions [ f(x) = f(-x) for all x); (iv) the set of all odd functions If(x) = -f(-x) for all x]; (v) the set of all functions f with f(0) = 0; (vi) the set of all functions f with f(0) = 1; (vii) the set of all non-negative functions (f (3) 0 for all x). 2.6. Show that the space C[-1, 1) defined in the preceding exercise is the direct sum of the subspaces determined by the descriptions (iii) and (iv).