Chapter 4 - Vector Spaces - 4.5 Linear Dependence and Linear Independence - True-False Review - Page 296: c

False

We know a $7 \times 5$ matrix has 7 rows and 5 columns, so there will be five column-vectors in the matrix. The vectors are elements of $R^7$, then we also have five vectors in five-dimensional space. Since matrix $A$ can be taken with same entries in each column, the set of column vectors of a $7 \times 5$ matrix A can not be linearly dependent.