please answer 15 10 Find the eigenvalues of C Consider the ma C c, cz c, The set

Question

please answer 15

10 Find the eigenvalues of C Consider the ma C c, cz c, The set of all real valued functions is a vector space, let's denote it as tr, The vectors in this space are functions f-f(x) defined for all real x with these operations f. g f(r) +g(x) k f(x) k a scalar (any real number) For these questions, determine if the described set is a subspace of F r) 12, All f f(r) such that f(o)-1 11. All f f(x) such that f( for all x x)s0 13. All near functions that is, f -f(x) such that fl Ax +B This set S is not a basis for R but it definitely spans R Because of this, you will be able to express the given vector v as a linear combination of the vectors in S in at least two different ways. Show me two. and v 14, S 15, For which value(s of n will V be linearly dependent?

Explanation / Answer

a(n) +b(-0.5) +c(-0.5) =0 -------------1

b(n) +a(-0.5) +c(-0.5) =0 --------------2

c(n) +b(-0.5) +a(-0.5) =0 ------------3

eqn 2 - eqn 1 : b(n + 0.5) -a(n +0.5) =0 : (n +0.5)(b-a) =0

eqn 3 -eqn 2 : c(n + 0.5) - b (n +0.5)=0 : (n +0.5)(c-b) =0

eqn 1 - eqn 3 :a(n + 0.5) - c n +0.5)= 0 : (n+0.5)(a-c) =0

either n = -0.5 or a= b =c and n = 1

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