CHEN 3201 Lecture Notes - Lecture 4: Linear Combination, Matlab, Triangular Matrix
2 Feb 2015
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Problem 1: solve the following system of equations using gauss elimination: Want to reduce matrix in problem 1 so that above diagonal has #s and below has 0 sweep row column. # in parenthases = sweep # multiplying factor. Chen3201_numericalmethods page 3 this is how we type it into matlab. Chen3201_numericalmethods page 5 program could go wrong if have to divide by 0. -> can switch up rows to make sure that doesn"t happen. Chen3201_numericalmethods page 6: if two rows of a matrix are identical, deta = 0 --> true. 2 rows are independent: adding a multiple of 1 row to another leaves determinant unchanged --> true row 2 + row 1. Chen3201_numericalmethods page 7: determinant changes sign when rows are interchanged --> 2, determinant of upper triangular matrix = product of the entries on the diagonal --> true. Chen3201_numericalmethods page 8 (3)(1)(2) + 0 + 0 - 0 - 0 - 0 = 6: det(ab) = det(a)det(b) true.
