Given two vectors \(v_1\) and \(v_2\) and two scalers \(\lambda_1\) and \(\lambda_2\), the sum \(\lambda_1 v_1 + \lambda_2 v_2\) is called the linear combination of the vectors \(v_1\) and \(v_2\). The scalers \(\lambda_1\) and \(\lambda_2\) are called the coefficients of the linear combination.
If the vectors \(v_1\) and \(v_2\) are column vectors of a matrix \(A\), then the vector \(x = \begin{bmatrix}v_1 & v_2 \end{bmatrix} \begin{bmatrix}\lambda_1 \\ \lambda_2 \end{bmatrix}\) gives us the linear combination if the column vectors with the coefficients \(\lambda_1\) and \(\lambda_2\).