Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part80

Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part80

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Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition D 21 Copyright © Orchard Publications The Adjoint of a Matrix D.8 The Adjoint of a Matrix Let us assume that is an n square matrix and is the cofactor of . Then the adjoint of , denoted as , is defined as the n square matrix below. (D.41) We observe that the cofactors of the elements of the ith row (column) of are the elements of the ith column (row) of . Example D.12 Compute if Matrix is defined as (D.42) Solution: D.9 Singular and Non Singular Matrices An square matrix is called singular if ; if , is called non singular. A α ij a A adjA α 11 α 21 α 31 …α n1 α 12 α 22 α 32 n2 α 13 α 23 α 33 n3 …………… α 1n α 2n α 3n nn = A A A 123 134 143 = 34 43 23 14 13 12 7 61 10 1 1 == nA d e t A 0 = detA 0 A
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Appendix D Matrices and Determinants D 22 Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition Copyright © Orchard Publications Example D.13 Matrix is defined as (D.43) Determine whether this matrix is singular or non singular. Solution: Therefore, matrix is singular. D.10 The Inverse of a Matrix If and are square matrices such that , where is the identity matrix, is called the inverse of , denoted as , and likewise, is called the inverse of , that is, If a matrix is non-singular, we can compute its inverse from the relation (D.44) Example D.14 Matrix is defined as (D.45) Compute its inverse, that is, find A A 123 234 357 = detA 12 23 35 21 24 30 27 20 28 ++ 0 == = A AB n A B B A I IB A 1 = 1 = AA 1 A 1 1 ------------adjA = A A 134 143 = A 1
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Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition D 23 Copyright © Orchard Publications The Inverse of a Matrix Solution: Here, , and since this is a non-zero value, it is possible to compute the inverse of using (D.44).
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This note was uploaded on 11/20/2009 for the course EE EE 102 taught by Professor Bar during the Fall '09 term at UCLA.

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Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part80

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