Assume that {u, v} is independent in a vector space V. Write uʹ = au + bv

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Assume that {u, v} is independent in a vector space V. Write uʹ = au + bv and vʹ = cu + dv, where a, b, c, and d are numbers. Show that {uʹ, vʹ} is independent if and only if the matrix
ac bd

is invertible.

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