For example 2 1 4 0 3 −1 0 0 −2 is an upper triangular matrix… Elementary Mathematics 3 Solution : (a) 31420 + 50261 + 47523 + 9431 + 23084 + 62100 = 223819 Answer : 223819. Problems (1) For this problem assume that … If the first element is zero the first make use of interchange. Null/Zero Matrix A matrix of any order, having all its elements are zero, is called a null/zero matrix. The numbers are written side by side putting plus sign (+) in between them. Matrices I. A square matrix A= [aij] is said to be an lower triangular matrix if aij = 0 for i Semantic Scholar's Logo. 1.2 Elementary Row Operations Example 1.2.1 Find all solutions of the following system : x + 2y z = 5 3x + y 2z = 9 x + 4y + 2z = 0 In other (perhaps simpler) examples we were able to nd solutions by simplifying the system (perhaps by eliminating certain variables) through operations of the following types : 1. Search. Matrices are used mainly for representing a linear transformation from a vector field to itself. The roots of this polynomial are the eigenvalues of the matrix. Lecture 9: Elementary Matrices Review of Row Reduced Echelon Form Consider the matrix A and the vector b de ned as follows: A = 1 2 3 8 b = 1 5 A common technique to solve linear equations of the form Ax = b is to use Gaussian elimination.