notes II
... The nullspace of A is defined by solutions to A.x = 0. If we transform A.x = 0 to U.x = 0 by a set of row operations then it is obvious that solutions to U.x = 0 must be the same as those to A.x = 0 and so the nullspace of A is the same as the nullspace of U. It has dimension n – r (nullity), i.e. t ...
... The nullspace of A is defined by solutions to A.x = 0. If we transform A.x = 0 to U.x = 0 by a set of row operations then it is obvious that solutions to U.x = 0 must be the same as those to A.x = 0 and so the nullspace of A is the same as the nullspace of U. It has dimension n – r (nullity), i.e. t ...
Properties of Matrices
... product of matrix T, the total amounts matrix, and matrix R, the cost matrix. To multiply these and get a 1 1 matrix, representing the total cost, requires multiplying a 1 4 matrix and a 4 1 matrix. This is why in part (b) a row matrix was written rather than a column matrix. The total materia ...
... product of matrix T, the total amounts matrix, and matrix R, the cost matrix. To multiply these and get a 1 1 matrix, representing the total cost, requires multiplying a 1 4 matrix and a 4 1 matrix. This is why in part (b) a row matrix was written rather than a column matrix. The total materia ...
