tailieunhanh - Electric Circuits, 9th Edition P75

Electric Circuits, 9th Edition P75. Designed for use in a one or two-semester Introductory Circuit Analysis or Circuit Theory Course taught in Electrical or Computer Engineering Departments. Electric Circuits 9/e is the most widely used introductory circuits textbook of the past 25 years. As this book has evolved over the years to meet the changing learning styles of students, importantly, the underlying teaching approaches and philosophies remain unchanged. | 716 The Solution of Linear Simultaneous Equations If we let C adj A A and use the technique illustrated in Section we find the elements of C to be cn 9 - 21 4 -8 c12 18 - 14 - 4 0 c13 27 - 7 - 20 0 c21 -16 24 - 8 0 c 22 32 16 8 8 c23 48 8 40 0 c31 5 - 9 4 0 c32 10 - 6 - 4 0 c33 15 - 3 - 20 -8. Therefore detA-U. A square matrix A has an inverse denoted as A-1 if A-1 A AA-1 U. Equation tells us that a matrix either premultiplied or postmultiplied by its inverse generates the identity matrix U. For the inverse matrix to exist it is necessary that the determinant of A not equal zero. Only square matrices have inverses and the inverse is also square. A formula for finding the inverse of a matrix is _ adj A det A The formula in Eq. becomes very cumbersome if A is of an order larger than 3 by Today the digital computer eliminates the drudgery of having to find the inverse of a matrix in numerical applications of matrix algebra. It follows from Eq. that the inverse of the matrix A in the previous example is A 1 1 8 9 -16 5 -7 4 8 8 -3 4 2-1-1 You should verify that A-1A AA U. 2 You can learn alternative methods for finding the inverse in any introductory text on matrix theory. See for example Franz E. Hohn Elementary Matrix Algebra New York Macmillan 1973 . Partitioned Matrices 717 Partitioned Matrices It is often convenient in matrix manipulations to partition a given matrix into submatrices. The original algebraic operations are then carried out in terms of the submatrices. In partitioning a matrix the placement of the partitions is completely arbitrary with the one restriction that a partition must dissect the entire matrix. In selecting the partitions it is also necessary to make sure the submatrices are conformable to the mathematical operations in which they are involved. For example consider using submatrices to find the product C AB where 4 5 2 1 -3 1 0 1 -2 0 and 2 0 -1 3 0 Assume that we