Mathematics 2B - TU01 - True/False

1. The vector \(\begin{bmatrix} 1 \\ 1 \end{bmatrix}\) can be written as a linear combination of the vectors \(\begin{bmatrix} 1 \\ 0 \end{bmatrix}\) and \(\begin{bmatrix} 4 \\ 0 \end{bmatrix}\).

2. A system of linear equations with augmented matrix \([A|\mathbf{b}]\) hasa unique solution if and only if \(\mathbf{b}\) is a linear combination of the columns of A.