Quantum Mechanics: Concepts and Applications · Problem 2.2

Mathematical Tools of Quantum Mechanics — Nouredine Zettili

Physics — Quantum Mechanics · linear-independence-vectors

Problem

Are the following sets of vectors (in the three-dimensional Euclidean space) linearly independent or dependent? (a) A⃗=(3,0,0)\vec{A} = (3, 0, 0), B⃗=(0,−2,0)\vec{B} = (0, -2, 0), C⃗=(0,0,−1)\vec{C} = (0, 0, -1) (b) A⃗=(6,−9,0)\vec{A} = (6, -9, 0), B⃗=(−2,3,0)\vec{B} = (-2, 3, 0) (c) A⃗=(2,3,−1)\vec{A} = (2, 3, -1), B⃗=(0,1,2)\vec{B} = (0, 1, 2), C⃗=(0,0,−5)\vec{C} = (0, 0, -5) (d) A⃗=(1,−2,3)\vec{A} = (1, -2, 3), B⃗=(−4,1,7)\vec{B} = (-4, 1, 7), C⃗=(0,10,11)\vec{C} = (0, 10, 11), and D⃗=(14,3,−4)\vec{D} = (14, 3, -4)

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