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A coordinate pair specifies the coefficients of a linear combination of the basis vectors. Without knowing the ordered basis, the numbers 3 and 2 do not tell you which vectors to scale and add.

Conditions: The vector space is equipped with a chosen ordered basis.; Coordinates are interpreted as coefficients of that basis.

A coordinate pair specifies the coefficients of a linear combination of the basis vectors. Without knowing the ordered basis, the numbers 3 and 2 do not tell you which vectors to scale and add.

Conditions: The vector space is equipped with a chosen ordered basis.; Coordinates are interpreted as coefficients of that basis.