Chapter 2. The solution of linear Systems AX-B
Chapter 2. The Solution of Linear Systems AX=B
2.1 Introduction to vectors and Matrices
2.1 Introduction to Vectors and Matrices
2.2 Properties of Vectors and Matrices
2.2 Properties of Vectors and Matrices
2. 3 Upper-triangular Linear Systems
2.3 Upper-triangular Linear Systems
Definition 2.2. An N X N matrix A= a;i) is called upper triangular provided that the elements satisfy ai=0 whenever i>j. The N X N matrix A=ail is called lower triangular provided that ai=0 whenever i< j 1x1+a12x2+a133+…+a1N-1xN-1+a1NxN=b1 222+a23x3+…+a2N-1xN-1+a2NxN=b2 a33 3+.+a3N-1N-1+a3NCN=b3 aN___1+aN_INCN= bN-1 aNNeN=b