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Suppose that v, w are orthogonal vectors and that u = cv + dw. Compute u middot v and use the result to find c. Compute u middot w and use the result to find d. (So far, everything is a variable.) Let v = (1 2) and w = (2 -1). Note that v, w are orthogonal. Let u = (5 6) Find the coefficients c and d for which u = cv + dw. We can do the same thing in matrix form. Remember that if a matrix Q has orthogonal columns then Q^T Q is diagonal. Part (c) of the previous problem amounts to solving (1 2 2 -1) (c d) = (5 6) Multiply both sides by Q^T to get a matrix equation involving a diagonal matrix Q^T Q. Then solve to find c, d.

Solve for u. Q = c/1 - u u =