Suppose a is a 7 times * 5 matrix. how many pivot columns must a have if its columns are linearly independent? why?

A matrix 7 * 5 means a matrix of 7 rows and 5 columns.

The matrix can only have 5 pivot columns for the system to be linearly independent.

Remember that in the system of equations:

Ax = b

A is the coefficient matrix of the incognita vector x and b is the solution vector.

The extended matrix is

(A l b)

If the matrix has more than 5 pivot columns, then the system is linearly dependent.