A First Course in Linear Algebra · Problem RQ-B-2

Vector Spaces — Robert Beezer

Mathematics — Linear Algebra · bases-linear-combinations

Problem

Write the vector

\mathbf{w} = \begin{bmatrix}6\\6\\15\end{bmatrix}

as a linear combination of the columns of the matrix

A = \begin{bmatrix}-3 & 0 & 1\\1 & 2 & 1\\5 & 1 & 6\end{bmatrix}

How many ways are there to answer this question?