Question

Determine if the function defines an inner product on R³, where u = (u?, u?, u?) and v = (v?, v?, v?). (Select all that apply.) (u, v) = u?²v?² + u?²v?² + u?²v?² satisfies (u, v) = (v, u) does not satisfy (u, v) = (v, u) satisfies (u, v + w) = (u, v) + (u, w) does not satisfy (u, v + w) = (u, v) + (u, w) satisfies c(u, v) = (cu, v) does not satisfy c(u, v) = (cu, v) satisfies (v, v) ? 0, and (v, v) = 0 if and only if v = 0 does not satisfy (v, v) ? 0, and (v, v) = 0 if and only if v = 0

          Determine if the function defines an inner product on R³, where u = (u?, u?, u?) and v = (v?, v?, v?). (Select all that apply.)
(u, v) = u?²v?² + u?²v?² + u?²v?²
satisfies (u, v) = (v, u)
does not satisfy (u, v) = (v, u)
satisfies (u, v + w) = (u, v) + (u, w)
does not satisfy (u, v + w) = (u, v) + (u, w)
satisfies c(u, v) = (cu, v)
does not satisfy c(u, v) = (cu, v)
satisfies (v, v) ? 0, and (v, v) = 0 if and only if v = 0
does not satisfy (v, v) ? 0, and (v, v) = 0 if and only if v = 0

Determine if the function defines an inner product on R³, where u = (u?, u?, u?) and v = (v?, v?, v?). (Select all that apply.)
(u, v) = u?²v?² + u?²v?² + u?²v?²
satisfies (u, v) = (v, u)
does not satisfy (u, v) = (v, u)
satisfies (u, v + w) = (u, v) + (u, w)
does not satisfy (u, v + w) = (u, v) + (u, w)
satisfies c(u, v) = (cu, v)
does not satisfy c(u, v) = (cu, v)
satisfies (v, v) ? 0, and (v, v) = 0 if and only if v = 0
does not satisfy (v, v) ? 0, and (v, v) = 0 if and only if v = 0

Added by James T.

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