LINEAR TRANSFORMATIONS
... Proof. Suppose that A is row-reduced to row-echelon form. Then the columns of A corresponding to the leading columns of the reduced matrix form a basis for range(A), hence rank(A) is equal to the number of leading columns. The nonleading columns of the reduced matrix correspond to the parameters of ...
... Proof. Suppose that A is row-reduced to row-echelon form. Then the columns of A corresponding to the leading columns of the reduced matrix form a basis for range(A), hence rank(A) is equal to the number of leading columns. The nonleading columns of the reduced matrix correspond to the parameters of ...
Chapter 3: The Inverse
... ii) To construct an elementary matrix that multiplies the ith row of a matrix by the nonzero scalar k, replace the unity element in the i-i poistion of the identity matrix of appropriate order with the scalar k. iii) To construct an elementary matrix that adds to the jth row ofa matrix k times the i ...
... ii) To construct an elementary matrix that multiplies the ith row of a matrix by the nonzero scalar k, replace the unity element in the i-i poistion of the identity matrix of appropriate order with the scalar k. iii) To construct an elementary matrix that adds to the jth row ofa matrix k times the i ...
