Chapter 4 - Vector Spaces - 4.3 Exercises - Page 215: 3

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Let the three given vectors form the columns of a matrix A. Row reducing to reduced echelon form, we get $A=\begin{bmatrix}1&0&4.5\\0&1&-2.5\\0&0&0\end{bmatrix}$. Because it does not have a pivot in each row, it does not span $R^3$ nor or they linearly independent. Because we need 3 linearly independent vectors to produce a basis for $R^3$, this set is not a basis for $R^3$.