1.3.3 Rank of a Matrix
Chapter 1: Chapter 1 · MATHEMATICS-VOLUME 1 · EN medium
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To define the rank of a matrix, we have to know about sub-matrices and minors of a matrix. Let A be a given matrix. A matrix obtained by deleting some rows and some columns of A is called a sub-matrix of A . A matrix is a sub-matrix of itself because it is obtained by leaving zero number of rows and zero number of columns. Recall that the determinant of a square sub-matrix of a matrix is called a minor of the matrix. Definition . The rank of a matrix A is defined as the order of a highest order non-vanishing minor of the matrix A . It is denoted by the symbol ρ ( ). A The rank of a zero matrix is defined to be . Note (i) If a matrix contains at-least one non-zero element, then ρ ( )
📖 Class 12 Mathematics English Volume 1 2025 Edition www.tntextbooks.in · Page 27
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To define the rank of a matrix, we have to know about sub-matrices and minors of a matrix. Let A be a given matrix. A matrix obtained by deleting some rows and some columns of A is called a sub-matrix of A . A matrix is a sub-matrix of itself because it is obtained by leaving zero number of rows and zero number of columns.
Recall that the determinant of a square sub-matrix of a matrix is called a minor of the matrix. Definition . The rank of a matrix A is defined as the order of a highest order non-vanishing minor of the matrix A . It is denoted by the symbol ρ ( ).
A The rank of a zero matrix is defined to be . Note (i) If a matrix contains at-least one non-zero element, then ρ ( )
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