Ivan Shishkin, Rye (1878)

Problems/Linear algebraExercise

Forme linéaire et base

by Ancient Tree·
28
Difficulty scaleÉchelle de difficulté

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
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
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ReviewedReviewed by darktoaster
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Soit φ\varphi une forme linéaire sur R3\R^{3} telle que :
φ(1,0,0)=10,φ(0,1,0)=5,φ(0,0,1)=−1.\varphi(1,0,0)=10,\qquad \varphi(0,1,0)=5,\qquad\varphi(0,0,1)=-1.

Déterminer φ(2,3,4)\varphi(2,3,4).

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Solution by darktoaster

Discussions10 useful votes

φ(2,3,4)=φ(2⋅(1,0,0)+3⋅(0,1,0)+4⋅(0,0,1))\varphi(2,3,4) = \varphi( 2 \cdot (1,0,0) + 3 \cdot (0,1,0) + 4 \cdot (0,0,1))
φ(2,3,4)=2φ(1,0,0)+3φ(0,1,0)+4φ(0,0,1)\varphi(2,3,4) = 2 \varphi(1,0,0) + 3 \varphi(0,1,0) + 4\varphi(0,0,1)
φ(2,3,4)=2⋅10+3⋅5+4⋅(−1)\varphi(2,3,4)= 2 \cdot 10 + 3 \cdot 5 + 4 \cdot (-1)
φ(2,3,4)=31\varphi(2,3,4)=31

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