Ivan Shishkin, Rye (1878)

Problems/Linear algebraExerciseUnreviewed

Un exemple de projection

by FiniteField·
32
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This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
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Soit (P)(P) le plan de R3\mathbb{R}^3 d’équation x−y−2z=0x-y-2z=0 et uu le vecteur (1,2,1)T(1,2,1)^T.

  1. Calculer la matrice de la projection vectorielle sur (P)(P) parallèlement à uu.
  2. Calculer l’image par cette projection de la droite D ⁣:{x−y+z=02x+y−2z=0D\colon\left\{\begin{array}{rl}x-y+z&=0\\2x+y-2z&=0\end{array}\right..
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References

  1. Oral Mines-Ponts filière PSI 2023 (RMS 134-1 925)
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