MATH1002 Lecture Notes - Lecture 9: Elementary Matrix, Invertible Matrix, Augmented Matrix
20 Aug 2018
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For a 2 x 2 matrix a det(a) = ad - bc. Then the matrix is set out as follows. B] it is not always possible to attain the identity matrix (in this n case the matrix is not invertible): a-1= b. This system is homogenous: rref of a is i n. Elementary matrices: a is the product of elementary matrices. An n x n elementary matrix e is elementary if it can be obtained from iby only one elementary row operation. Different notation depending on the row operation performed. Then b = e a considering that e is obtained by performing the same operation on the. R r + r n ij j i i identity matrix. If we have a some series of elementary row operations b. Then there exists e, e, e elementary matrices such that b = e e. Moreover, the inverse matrix of an elementary matrix is elementary.
