Consider the subspace spanned by A ---- and 7₂ and the vector = basis {1, ₂}. = 5 9 in this subspace. Find the coordinates [] of the vector in the

Suppose that V is a that has subspaces of U and W. Furthermore, suppose that {u¹, u2} is a basis for U, that {1, 2} is a basis for W and that the only vector that U and W have in common is the zero vector 0. Show that {u¹, u², w¹, w²}. After you get done, note where you used the fact that the only vector common to both U and W is 0. (Without this condition the vectors {u¹, u², w², w2} don't need to be linearly independent, so if you didn't use this condition you definitely made a mistake somewhere.)

Find the distance from the point x = (1, 5, -4) of R to the subspace W consisting of all vectors of the form (a, a, b).

Find an orthonormal basis for the span: