A tensor and vector have components Tαβγ, and vα respectively in a coordinate system xμ. There is another coordinate system x'μ. Show that Tαβγvβ = Tαβγvβ
umm not sure...
∇αvβ = ∂vβ/∂xα - Γγαβvγ
The Attempt at a Solution
Tαβγvβ = (∂xα/∂xi*∂xj/∂xβ*∂xγ/∂xk*Tijk)(∂xβ/∂xa*va)
Tαβγvβ = (∂xα/∂xi*∂xβ/∂xj*∂xγ/∂xk*Tijk)(∂xa/∂xβ*va)
and the two are not equal which they should be. I really don't know where I've went wrong...