Transcription of NotesonMathematics-1021 - IIT Kanpur
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NotesonMathematics-1021 - IIT Kanpur
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.
Chapter 1 Matrices 1.1 Definition of a Matrix Definition 1.1.1 (Matrix) A rectangular array of numbers is called a matrix. We shall mostly be concerned with matrices having real numbers as entries.
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