Assume that u, v is independent in a vector space V Write u Ecirc sup1 au bv and v Ecirc sup1 cu dv, where a, b, c, and d are numbers Show that u Ecirc sup1 , v Ecirc sup1 is independent if and only if the matrix is invertible ac bd

Question: Assume that {u, v} is independent in a vector space V. Write uÊ¹ = au + bv and vÊ¹ = cu + dv, where a,

Assume that {u, v} is independent in a vector space V. Write uÊ¹ = au + bv and vÊ¹ = cu + dv, where a, b, c, and d are numbers. Show that {uÊ¹, vÊ¹} is independent if and only if the matrix

is invertible.

ac bd

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