Final answer:
The statement is false; the Gram-Schmidt process does indeed yield an orthonormal basis for a subspace W after vectors are normalized. Wave-particle duality pertains to microscopic particles, not macroscopic objects.
Step-by-step explanation:
The statement, 'The Gram-Schmidt process applied on a basis of a subspace W does not necessarily yield an orthonormal basis for W', is false. The Gram-Schmidt process is specifically designed to produce an orthogonal basis from a set of linearly independent vectors in a subspace W. However, to convert this orthogonal basis into an orthonormal basis, each vector must be normalized by dividing by its norm. Therefore, the process does yield an orthonormal basis provided the additional step of normalization is taken. Addressing the GRASP CHECK question, if only the angles of two vectors are known, the angle of their resultant addition vector cannot be found without additional information, so the answer is false. As for the wave-particle duality question, it states that wave-particle duality exists for objects on the macroscopic scale. The correct answer is false, as wave-particle duality is a phenomenon that is observable for microscopic particles, such as electrons, but not for macroscopic objects that we see in the everyday world.