What is the purpose of step three after column reduction?

To select independent zeros, scan the reduced matrix for rows or columns with only one available zero. Circle that zero and strike out other zeros in the same row and column.

Conditions: The matrix has been reduced using row and column operations.; The goal is to find n independent zeros for an n x n matrix.

The presenter avoids selecting a zero when a row has two zeros because the goal is to find a set of independent zeros where each row and column has exactly one selected zero. Choosing arbitrarily from a row with multiple zeros might lead to conflicts later, so the process is postponed until the zero pattern is more constrained.

Conditions: The matrix has undergone row and column reduction.; The goal is to find an optimal assignment.

A balanced assignment problem means that the number of rows (persons) is equal to the number of columns (jobs). This allows for a one-to-one assignment where each person is assigned to exactly one job.

Conditions: The cost matrix is square (same number of rows and columns).; Each job is to be assigned to exactly one person.

Column reduction is the second step of the Hungarian method. It involves taking the matrix obtained after row reduction, finding the minimum element in each column, and subtracting this minimum value from all elements in that same column.

Conditions: The matrix must have already undergone row reduction.; The problem is a balanced assignment problem.

To calculate the total cost, you must look at the original cost matrix, not the reduced matrix. Identify the positions of the circled zeros in the reduced matrix, find the corresponding entries in the original matrix, and sum those values.

Conditions: The optimal assignment has been determined from the reduced matrix.; The original cost matrix is available.