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We investigate the determinantal representation by exploiting the limiting expression for the generalized inverse AT,S(2). We show the equivalent relationship between the existenceand limiting expression of AT,S(2) and some limiting processes of matrices and deduce the new determinantalrepresentations of AT,S(2), based on some analog of the classical adjoint matrix. Using theanalog of the classical adjoint matrix, we present Cramer rules for the restricted matrix equation AXB=D,  R(X)⊂T,  N(X)⊃S∼

mathematical problems in engineering

An Analog of the Adjugate Matrix for the Outer Inverse<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mi>A</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mo>,</mml:mo><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mrow></mml:math>

An Analog of the Adjugate Matrix for the Outer InverseAT,S(2)