线性代数问题,求图中题的思路,好的追分,谢谢!
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线性代数问题,求图中题的思路,好的追分,谢谢!
请介绍下解题过程,谢谢!
晚上回答.
你等一下.
再问: ....好的亲 ^___^
再答: wong6764的答案第一问是正确的,但二、三问做得有点问题。∵rot(F)=∇×F=(∂/∂x,∂/∂y,∂/∂z)×(y^2,-z^2,x^2)=2(z,-x,-y)≠0∴F is not conservative又∵rot(G)=∇×G=(∂/∂x,∂/∂y,∂/∂z)×(x^3-3xy^2,y^3-3x^2y,z)=0 ∴G is conservative2.G's Potential function: ∵(x^3-3xy^2)dx+(y^3-3x^2y)dy+zdz=x^3dx-3xy^2dx+y^3dy-3x^2ydy+zdz =d[(1/4)x^4+(1/4)y^4-(3/2)x^2y^2+(1/2)z^2] u=(1/4)x^4+(1/4)y^4-(3/2)x^2y^2+(1/2)z^2 ∴Potential function v=-u+c=-[(1/4)x^4+(1/4)y^4-(3/2)x^2y^2+(1/2)z^2]+c3.(对不起,有事去了,如果没人给出正确答案,稍后继续)
你等一下.
再问: ....好的亲 ^___^
再答: wong6764的答案第一问是正确的,但二、三问做得有点问题。∵rot(F)=∇×F=(∂/∂x,∂/∂y,∂/∂z)×(y^2,-z^2,x^2)=2(z,-x,-y)≠0∴F is not conservative又∵rot(G)=∇×G=(∂/∂x,∂/∂y,∂/∂z)×(x^3-3xy^2,y^3-3x^2y,z)=0 ∴G is conservative2.G's Potential function: ∵(x^3-3xy^2)dx+(y^3-3x^2y)dy+zdz=x^3dx-3xy^2dx+y^3dy-3x^2ydy+zdz =d[(1/4)x^4+(1/4)y^4-(3/2)x^2y^2+(1/2)z^2] u=(1/4)x^4+(1/4)y^4-(3/2)x^2y^2+(1/2)z^2 ∴Potential function v=-u+c=-[(1/4)x^4+(1/4)y^4-(3/2)x^2y^2+(1/2)z^2]+c3.(对不起,有事去了,如果没人给出正确答案,稍后继续)