Final answer:
The maximum possible value for the nullity of a 4x7 matrix is 3.
Step-by-step explanation:
The maximum possible value for the nullity of a 4x7 matrix is 3.
The nullity of a matrix is defined as the dimension of its null space, which is the set of all solutions to the equation Ax = 0, where A is the matrix and x is a column vector of appropriate size.
In this case, since the matrix is 4x7, the nullity cannot exceed the smaller dimension, which is 4. Therefore, the maximum possible value for the nullity is 3, which occurs when the matrix has 3 linearly independent columns.