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AI & ML · Linear Algebra

Projections & orthogonality

144 problems in this skill, each with a solver-verified answer key. Answers are checked the moment you submit — with a hint if you want one and a worked solution afterwards.

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A few statements from this skill. Answers, hints and worked solutions live in the practice session.

  1. Warm-up

    Vectors u⃗=(−2,3)\vec u = (-2, 3) and v⃗=(x,2)\vec v = (x, 2) are orthogonal, i.e. u⃗⋅v⃗=0\vec u \cdot \vec v = 0. Find xx.

  2. Warm-up

    Vectors u⃗=(−3,−1)\vec u = (-3, -1) and v⃗=(x,3)\vec v = (x, 3) are orthogonal, i.e. u⃗⋅v⃗=0\vec u \cdot \vec v = 0. Find xx.

  3. Warm-up

    Vectors u⃗=(3,4)\vec u = (3, 4) and v⃗=(x,3)\vec v = (x, 3) are orthogonal, i.e. u⃗⋅v⃗=0\vec u \cdot \vec v = 0. Find xx.

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