
Thank you in advance
its asking to find a value y in V for which g(x) = <x,y> , for all x in V

Thank you in advance its asking to find a value y in V for which g(x)...
I need some help, thank you in advance.
1. For each of the following inner product spaces V and linear transformations g, find a value of ye V for which g(x) = (1,y), for all z e V. (i) V = P2 (R) with (8,9) = S slog(t) dt and g: VR defined by g(f) = f'(0) + 2f(1). (ii) V = M2x2(C) with the Frobenius inner product, and g :V → C defined by g(A) = tr 1+ 1...
Part 2 please !
1. For each of the following inner product spaces V and linear transformations g, find a value of y € V for which g(x) = (x,y), for all 2 € V. (i) V = P2(R) with f(t)g(t) dt and g: V + R defined by g(f) = f'(0) + f(1). (ii) V = M2x2(C) with the Frobenius inner product, and g: VC defined by 1 g(A) = tr
1. For each of the following inner product spaces V and linear transformations g, find a value of y € V for which g(x) = (x, y), for all x € V. (i) V = P2(R) with f(t)g(t) and g: V+ R defined by g(s) = f'(0) +2f(1). (ii) V = M2x2(C) with the Frobenius inner product, and g: V+C defined by i g(A) =tr :((1141 - :)4).
1. For each of the following inner product spaces V and linear transformations g, find a value of y € V for which g(x) = (x, y), for all 1 € V. (i) V=P2(R) with f(t)g(t) dt and g: V + R defined by g(f) = f'(0) + 2f (1). (ii) V = M2x2(C) with the Frobenius inner product, and g:V + C defined by i i g(A) = tr (( 1 1 1
I need some help. thank you.
3. Consider the inner product space V = M2x2(C) with the Frobenius inner product, and let T:V V be the linear operator defined by T(A) = A. (i) Compute T* (ii) Determine whether or not there is an orthonormal basis of eigenvectors B for which [T]e is diagonal. If such a basis exists, find one.
Part 2 please !!
3. Consider the inner product space V = M2x2(C) with the Frobenius inner product, and let T:V + V be the linear operator defined by T(4) = ( ; A. (i) Compute "((1+i (ii) Determine whether or not there is an orthonormal basis of eigenvectors 8 for which (T), is diagonal. If such a basis exists, find one.
3. Consider the inner product space V = M2x2(C) with the Frobenius inner product, and let T:V → V be the linear operator defined by 0 T(1) = ( ; ;) A. (i) Compute To((.) (ii) Determine whether or not there is an orthonormal basis of eigenvectors B for which [T]is diagonal. If such a basis exists, find one.
3. Consider the inner product space V = M2x2(C) with the Frobenius inner product, and let T:V + V be the linear operator defined by T(A) -1 (i) Compute T:((1+i :)) (ii) Determine whether or not there is an orthonormal basis of eigenvectors 8 for which [T], is diagonal. If such a basis exists, find one.
I need help with this one, thank you in advance
2. Consider the inner product space V = P2(R) with (5.9) = L 109(e) dt, and let T:V – V be the linear operator defined by T(S) = If'(x) + 2%(r) +1. (i) Compute T*(1+1+z?). (ii) Determine whether or not there is an orthonormal basis of eigenvectors B for which Tja is diagonal. If such a basis exists, find one.
Let V be a finite dimensional vector space over R with an inner product 〈x, y〉 ∈ R for x, y ∈ V . (a) (3points) Let λ∈R with λ>0. Show that 〈x,y〉′ = λ〈x,y〉, for x,y ∈ V, (b) (2 points) Let T : V → V be a linear operator, such that 〈T(x),T(y)〉 = 〈x,y〉, for all x,y ∈ V. Show that T is one-to-one. (c) (2 points) Recall that the norm of a vector x ∈ V...