4. Assume that a matrix A satisfies PA = LU, where0011 0 0100(19)010-P =L =and U =231012002Use these factors, without forming the matrix A or taking any inverses,to solve the system of equations Ax = b, where b = (2, 10, -12)T. Showforward and back substitution by hand.

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Answered: 4. Assume that a matrix A satisfies P A…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose the above equation is expressed as Ax=b with x=(x1 x2 x3)express the cofficicents of the equations in one matrix form as (A|b)
Consider the following linear equations: -2x + 4y + 10z = -5 -2x + (22-k)y+9z = -3 -2x + 4y+(12-k)z =k+9 a) Suppose the above equation is expressed as Ax = b with x = equations in one matrix form as (Alb)= -2 -2 -2 4 -2 10 4 X3 10 -5 b) Use row operations on (Alb) by substracting row 1 from row 2 and row 3 respectively. Fill in the missing entries: Express the coefficients of the -5 Submit part 3 marks Unanswered
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4. Assume that a matrix A satisfies P A = LU, where 10 0 (19). 3 4 P=100 010 2 L = 231 10, and U = 012 002 Use these factors, without forming the matrix A or taking any inverses, to solve the system of equations Ax = b, where b = (2, 10, −12)T. Show forward and back substitution by hand.