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Lecture Notes

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.

10 CHAPTER 1. MATRICES Example 1.1.4 The linear system of equations 2x+ 3y= 5 and 3x+ 2y= 5 can be identified with the matrix " 2 3 : 5 3 2 : 5 #. 1.1.1 Special Matrices

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