Tutorial 1 Solutions - Tutorial 1 1104B Fall 2007 1 1.Find a Row Echelon Form and the Reduced Row Echelon Form of the following matrix 3 2 A= 1 4 n R1 =

Tutorial 1 1104B, Fall 2007 1. 1.Find a Row Echelon Form and the Reduced Row Echelon Form of the following matrix: A =    3 6 1 6 3 4 2 4 1 6 3 4 1 2 1 2 3 0 4 8 3 10 6 10    R n 1 = R 3 R n 3 = R 1    1 2 1 2 3 0 2 4 1 6 3 4 3 6 1 6 3 4 4 8 3 10 6 10    ∼ R n 2 = R 2 - 2 R 1 R n 3 = R 3 - 3 R 1 R n 4 = R 4 - 4 R 1    1 2 1 2 3 0 0 0 - 1 2 - 3 4 0 0 - 2 0 - 6 4 0 0 - 1 2 - 6 10    R n 2 = - R 2 R n 3 = - R 3 R n 4 = - R 4    1 2 1 2 3 0 0 0 1 - 2 3 - 4 0 0 2 0 6 - 4 0 0 1 - 2 6 - 10    ∼ R n 3 = R 3 - 2 R 2 R n 4 = R 4 - 4 R 2    1 2 1 2 3 0 0 0 1 - 2 3 - 4 0 0 0 4 0 4 0 0 0 0 3 - 6    This is my REF. Now for RREF. R n 3 = 1 4 R 3 R n 4 = 1 3 R 4    1 2 1 2 3 0 0 0 1 - 2 3 - 4 0 0 0 1 0 1 0 0 0 0 1 - 2    ∼ R n 1 = R 1 - R 2    1 2 0 4 0 4 0 0 1 - 2 3 - 4 0 0 0 1 0 1 0 0 0 0 1 - 2    ∼ R n 1 = R 1 - 4 R 3 R n 2 = R 2 + 2 R 3    1 2 0 0 0 0 0 0 1 0 3 - 2 0 0 0 1 0 1 0 0 0 0 1 - 2    ∼ R n 2 = R 2 - 3 R 4    1 2 0 0 0 0 0 0 1 0 0 4 0 0 0 1 0 1 0 0 0 0 1 - 2    1a. Find all possible basic and free variables of a system whose coeffcient matrix is A . Awnser: x 1 , x 3 , x 4 , and x 5 are basic variables and x 2