- Linear Algebra 1 (193.12 KiB) Viewed 32 times
Linear Algebra
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answerhappygod
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Linear Algebra
Linear Algebra
Problem! Let fui and Uz be two vectors in R³ 143 for the moment let i j k denoto the three standand besis vectores. So any vector, like u, can be written U = U₂₁ ₁ +4₂√ + 43₁ K ۱۴ The crossed product uxV is the vector LXV = det i k where this is shart hand Y₁ V₂. V₂ 141 4₂ из tt! for, if we were to expand along the top row, -2 det V/₂ + (-₁)+² j. det | x₁ + u₁ ++3. K dot V₁ 14₁ U₂ la) Fix u then V →UXV is a Linear map in X 3 3 from R² R. Find the matrix of this linear map with respect to the standard basis. (b) We know that matrix mult corresponds to composition of linear maps. Use this fact to show WX (ux V) # (WXL) X Y PW: (c) (Triple product) het W= W₂ W3 Show (w_ UxV) = det / W₁ W₂ Conclude that X3 Иг из V3 V₂ us V V₂ إلا W3 |Y₁ X₂ V3 FUT Uz u LuxV and ✓ Lux v
Problem! Let fui and Uz be two vectors in R³ 143 for the moment let i j k denoto the three standand besis vectores. So any vector, like u, can be written U = U₂₁ ₁ +4₂√ + 43₁ K ۱۴ The crossed product uxV is the vector LXV = det i k where this is shart hand Y₁ V₂. V₂ 141 4₂ из tt! for, if we were to expand along the top row, -2 det V/₂ + (-₁)+² j. det | x₁ + u₁ ++3. K dot V₁ 14₁ U₂ la) Fix u then V →UXV is a Linear map in X 3 3 from R² R. Find the matrix of this linear map with respect to the standard basis. (b) We know that matrix mult corresponds to composition of linear maps. Use this fact to show WX (ux V) # (WXL) X Y PW: (c) (Triple product) het W= W₂ W3 Show (w_ UxV) = det / W₁ W₂ Conclude that X3 Иг из V3 V₂ us V V₂ إلا W3 |Y₁ X₂ V3 FUT Uz u LuxV and ✓ Lux v
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