Answer to Question #258089 in Linear Algebra for Tege

Question

Write (12,22,1) as a linear combination of the vectors (0,2,1),(3,0,1),(5,6,0) if possible

Answer 1

It is possible to write (12,22,1) as a linear combination of the vectors (0,2,1), (3,0,1), (5,6,0):

$$\begin{bmatrix} 12 \\ 22 \\ 1 \end{bmatrix}=2\begin{bmatrix} 0 \\ 2 \\ 1 \end{bmatrix}+(-1)\begin{bmatrix} 3 \\ 0 \\ 1 \end{bmatrix}+3\begin{bmatrix} 5 \\ 6 \\ 0 \end{bmatrix}.$$