True/False 1) Decide if each of the following statements is true or false. Justify your conclusion with an explanation or counter-example, as appropriate. 1. Applying Gram-Schmidt to an orthogonal set of vectors returns the vectors unchanged. 2. A nonzero vector can be orthgonal to itself. 3. The intersection of a subspace and its orthogonal complement is trivial. 4. If (₁,...,) is an orthonormal basis for R" and w = a₁₁ + + av, then |w| = √a² + ... + a². 5. If a matrix U has orthonormal columns, then UUT = 1.

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