Question

QUESTION 1: 11 2 4 Find the inverse of A = 3 8 14] using LU Decomposition Method. 12 6 13) --

Answer 1

2 2 4 Given that the matrie 3 8 2 6 14 13 To find the inverse of matrix A by using LV Decomposition Method. First find the LU de composition A=LU * Find the inverse matrices for U and L > Now multiply O and I to get a We have inverse operator A = BC A' -'8"? A'=uta A ELU Let us find the Lu de composition by using Gauss Elimination. Elementary Row operations 오 4 on 8 14 2 6 2 0 2 R2 Rq (+3) R, R3 R3 -(2) Ra 2 2 o 5 1 2 4 Rg → 23-(11R2 T 2 2 3 Thus the upper triangular matrise с 2 U = 2 +NM

row opetations Which make hatrix to The Lower triangular matsixe can be written from the coefficients of elementary apper triangular massie The diagonal elements of Lower trianguslar matsin The Coefficients of row operations are shown in pasanthesis. (). Thus, the lower triangular is L. matxixis 1 3 2 1 A - LU The LU Decomposition of the matrice 2 4 1 2 4 O 2 오 38 14 0 2 O 3 2 6 13 L and .by ) Now, let us fina inverse for elimination using Gauss-Jordan dow operations Apply the on [LI] - 1 0 0 3 1 0 2 O O 0 0 -3 1 Re > R2 -3R, Rz7R3 -2R, O o -2 O 1 0 O 0 R> R3-R2 1 -3 ( 0 - 다.

:. The inverse of L is L -3 O - ! ) 24) 2 2 1 10 Apply Now opperations on (usi) o o 310 1 24 R2 / / R2 1 Rs 7 / R3 o o 3 - - B>R, -2R RqR2 - 2 o 0 o oping yang ingin 16 0 -- RR, -2R3 ! is The inverse of the marrin -23 U' ya 3 Lot Lot Now the is given as AGE inverse of -45 Y 13 Ana - The 7 / 7