Cofactor of an element $a_{ij}$ in |A|: $A_{ij} = (-1)^{i+j} M_{ij}$ $|A| = |\table a_{11},a_{12},a_{13};a_{21}, a_{22},a_{23};a_{31},a_{32},a_{33}|$ e.g. $A_{11} =(-1)^{1+1}M_{11} = |\table a_{22},a_{23}; a_{32}, a_{33}|$ Adjoint of a matrix, adj. A = Transpose of cofactor matrix i.e. A’ |A| = 0 -> singular matrix |A| ≠ 0 – > non-singular matrix Inverse of A, if A is square matrix and |A| ≠ 0: $A^{-1} = 1/{|A|} adj. A$ Multiplication of matrix by scalar: $A = |\table 1,2;3,4|$ $(-1)A =|\table -1,-2;-3,-4| $ i.e. all elements get multiplied by that scalar Multiplication of matrices: If columns of A = rows of B, then ...
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