Provide the space C3 with the standard inner product. Consider the linear subspace V = span...

 

Transcribed Image Text:

Provide the space C3 with the standard inner product. Consider the linear subspace V = span {(1, w, w), (1, w, w)}, where w = e2i/3 (a) Compute an orthonormal basis for V. (b) Compute the best approximation v V of the vector (1, -1, 1). Express your final answer as v = (1, w, w)+(1, w, w) where the complex numbers A and 2 are written in Cartesian form and as simple as possible. Provide the space C3 with the standard inner product. Consider the linear subspace V = span {(1, w, w), (1, w, w)}, where w = e2i/3 (a) Compute an orthonormal basis for V. (b) Compute the best approximation v V of the vector (1, -1, 1). Express your final answer as v = (1, w, w)+(1, w, w) where the complex numbers A and 2 are written in Cartesian form and as simple as possible.