# Suppose x = [ 2 1 1 ], y = [1 1 1], z = [1 2 3 ], u = [1 12 12],

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Suppose x = [ 2 -1 1 ], y = [1 1 -1], z = [1 2 3 ], u = [1 -1/2
1/2], v= [3/14 6/14 9/14], and suppose that w = span {x, y},
w\' = Span{y, z}. which of the following is true? The
orthogonal projection of z onto W is v. The orthogonal
projection of z onto W is z. The orthogonal projection of x
onto W\' is v. None of above. The orthogonal projection of
x onto W\' is u.
Solution
E) The orthogonal projection of x onto W\' is u.
because of the expansion of Dot product

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Suppose x = [ 2 -1 1 ], y = [1 1 -1], z = [1 2 3 ], u = [1 -1/2 1/2], v= [3/14 6/14 9/14], and suppose that w = span {x, y}, w\' = Span{y, z}. which of the following is true? The orthogonal projection of z onto W is v. The orthogonal projection of z onto W is z. The orthogonal projection of x onto W ...
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