Question

Let I denote the space of all infinite sequences of real numbers, where addition and scalar multiplication is defined componentwise: (a1, 22, ...) + (61, 62, ...) = (a1 + b1, 22+ b2, ...), a(a1, a2, ...) = (aa1, 002, ...), then this is a vector space (you do not have to verify this). Define the operators L, R: 1 7 by: L(a1, 22, 23, ...) = (a2, 23, 24,...), R(21, 22, 23, ...) = (0, 21, 22, ...), then these are linear operators on l. Do the following: i) Find the kernels of L and R. ii) Show that LOR=Id, but RoL #Id.

Answer 1

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