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Definition: A vector v is a linear combination of vectors v_1, v_2, … ,v_k if there are scalars c_1, c_2, … c_k such that v = (c_1)(v_1) + (c_2)(v_2) + ... + (c_k)(v_k). The scalars c_1, c_2, … , c_k are called the coefficients of the linear combination.
Source: Linear Algebra: A Modern Introduction, 3rd edition by David Poole (note-custom edition titled Matrix Algebra)