is basis for the subspace W. Step1: Start the Gram-Schmidt process from the first vector to get an orthogonal and then an orthonormal basis for W. ----- Answer: W₁ = 1 , W2 = is an orthonormal basis of W where a= b= 7₁d=[ are all integers. Step 2: Find the orthogonal projection of the vector u = on W using the Orthogonal Decomposition Theorem. -9 Answer: The orthogonal projection is i where e f= .h= Step 3: Find the distance of the vector u from W. Answer: The distance is where A= Note: A is an integer. d g= -3/2] 1 3 2 are all positive integers (and, as usual, the entries of the vector has no common divisor!)

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