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Find a basis of the vector subspace P = {(a, b, c): a, b, c. element R, a + c = 0, a + b - 3c = 0) of R^3. What is the dimension of P? Find the splitting field of x^2 + 3x + 3 over Q. Show that Q(3 - 4i) = Q(i) where i = Squareroot -1. Show transcribed image text Find a basis of the vector subspace P = {(a, b, c): a, b, c. element R, a + c = 0, a + b - 3c = 0) of R^3. What is the dimension of P? Find the splitting field of x^2 + 3x + 3 over Q. Show that Q(3 - 4i) = Q(i) where i = Squareroot -1.
Find a basis of the vector subspace P = {(a, b, c): a, b, c. element R, a + c = 0, a + b - 3c = 0) of R^3. What is the dimension of P? Find the splitting field of x^2 + 3x + 3 over Q. Show that Q(3 - 4i) = Q(i) where i = Squareroot -1.
Show transcribed image text Find a basis of the vector subspace P = {(a, b, c): a, b, c. element R, a + c = 0, a + b - 3c = 0) of R^3. What is the dimension of P? Find the splitting field of x^2 + 3x + 3 over Q. Show that Q(3 - 4i) = Q(i) where i = Squareroot -1.1
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Elin HesselLv2
24 Jan 2019