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

True

We know a $5\times 7$ matrix has 5 rows and 7 columns, so there will be seven column-vectors in the matrix. The vectors are elements of $R^5$, then we also have seven vectors in five-dimensional space. Since there is more vectors than the dimension of space, the set of column vectors of a $5×7$ matrix A must be linearly dependent.