Final answer:
A 5x7 matrix must have at least 5 pivot columns to span R⁵.
Step-by-step explanation:
A 5x7 matrix has 7 columns. If these columns span R⁵, it means that the columns of the matrix are linearly independent and can generate any vector in R⁵, which is a space of 5 dimensions. In order for a set of vectors to span a space, the number of vectors in the set must be equal to or greater than the dimension of the space. Therefore, in this case, the matrix must have at least 5 pivot columns.