Please show all steps clearly. Also please use m=0, f= 7 and l=5 in the equation above
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Please show all steps clearly. Also please use m=0, f= 7 and l=5 in the equation above and the solve accordingly.
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5) (10 pts) Another method to find inverse of a square matrix uses the following equation. 1 A-¹ det (A) [4₁] Where, [A] is the transpose of the matrix obtained when every element of matrix A is replaced by its cofactor. Clearly show the cofactor of every element, then the matrix [A₁;], and then [A₁]. For example, for the following matrix B, sample cofactors of elements b23 and b31 are shown; followed by the matrix of cofactors [B₁j]; followed by [B₁j]"; and then B-¹. Calculate A¹ using this method and check that you obtain the same answer as in the earlier question. 3 2 -11 8 -3 1 2 B = 1 0; det(B) = 19 (Verify; no need to show in your solution.). 2 Cofactor of b23 = B₂3 = (−1)²+³|³3 | = -9. Cofactor of b31 = B31 = (-1)³+¹|²¹|=8 By calculating cofactors of all the elements of B gives the following cofactor matrix. (Verify; no need to show in your solution.) 16 T This gives [B] =-2 [16 -2 25 [Buj] = -5 3 -9 8 -1 22] -5 8 3 -1 and B-¹ = 25 -9 22. 1 19 16 -5 -2 25 -9 ل 8 -1 22. 5) (10 pts) Another method to find inverse of a square matrix uses the following equation. 1 A-¹ det (A) [4₁] Where, [A] is the transpose of the matrix obtained when every element of matrix A is replaced by its cofactor. Clearly show the cofactor of every element, then the matrix [A₁;], and then [A₁]. For example, for the following matrix B, sample cofactors of elements b23 and b31 are shown; followed by the matrix of cofactors [B₁j]; followed by [B₁j]"; and then B-¹. Calculate A¹ using this method and check that you obtain the same answer as in the earlier question. 3 2 -11 8 -3 1 2 B = 1 0; det(B) = 19 (Verify; no need to show in your solution.). 2 Cofactor of b23 = B₂3 = (−1)²+³|³3 | = -9. Cofactor of b31 = B31 = (-1)³+¹|²¹|=8 By calculating cofactors of all the elements of B gives the following cofactor matrix. (Verify; no need to show in your solution.) 16 T This gives [B] =-2 [16 -2 25 [Buj] = -5 3 -9 8 -1 22] -5 8 3 -1 and B-¹ = 25 -9 22. 1 19 16 -5 -2 25 -9 ل 8 -1 22.
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3xoyG6Z 11 5x 2y 3Z 17 2x y 42 detA det A A cofactors ... View the full answer
Related Book For
Differential Equations and Linear Algebra
ISBN: 978-0131860612
2nd edition
Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West
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