Transcription of NotesonMathematics-1021
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NotesonMathematics-1021
Notes on Mathematics - 1021 Peeyush Chandra, A. K. Lal, V. Raghavendra, G. Santhanam1 Supported by a grant from MHRD2 ContentsI Linear Algebra71 Definition of a Matrix .. Special Matrices .. Operations on Matrices .. Multiplication of Matrices .. Some More Special Matrices .. Submatrix of a Matrix .. Block Matrices .. Matrices over Complex Numbers .. 172 Linear System of Introduction .. Definition and a Solution Method .. A Solution Method .. Row Operations and Equivalent Systems .. Gauss Elimination Method .. Row Reduced Echelon Form of a Matrix .. Gauss-Jordan Elimination .. Elementary Matrices .. Rank of a Matrix .. Existence of Solution ofAx=b.. Example .. Main Theorem .. Exercises .. Invertible Matrices .. inverse of a Matrix .. Equivalent conditions for Invertibility.
Definition 1.2.7 (Additive Inverse) Let Abe an m×nmatrix. 1. Then there exists a matrix Bwith A+ B= 0.This matrix Bis called the additive inverse of A,and is denoted by −A= (−1)A. 2. Also, for the matrix 0m×n,A+0 = 0+A= A.Hence, the matrix 0m×n
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