A. SOLUTION OF NON-HOMOGENEOUS SYSTEMGIVEN:7-3 40-7A = 2 1 - 1 4 610 -3 -51. SOLVE THE SYSTEM USING GAUSSIAN ELIMINATION1.1 TRANSFORM TO UPPER TRIANGULAR MATRIX.1.2 TRANSFORM TO LOWER TRIANGULAR MATRIX.1.3 USE ROW-ECHELON FORM (UPPER TRIANGULAR)

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Answered: A. SOLUTION OF NON-HOMOGENEOUS SYSTEM…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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3 Using matrix diagonalisation, solve the following system of first order difference equations: Xn+1 = 6xn + Yn Yn+1 = 5x + 2yn with initial conditions to = 1 and yo = -1.
Given:2a + 5b + 3c = 23a + b - 2c = 3-a + 2b + c = 1Identify the coefficient matri A and the augmented matrix A'of the given linear system.
Do 2b)
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A. SOLUTION OF NON-HOMOGENEOUS SYSTEM GIVEN: 7 -3 4 0 -7 A = 2 1 -1 4 6 010-3 -3 -5 1.2 TRANSFORM TO LOWER TRIANGULAR MATRIX.
5. Solve the system of equations 3z-2z + 2z = 10 a + 2 - 3z, = -1 4 + za+2, = 3 %3D (a) by Cramer's rule and (b) by using inverse matrices.
1. A system of linear equations can be described in a matrix equation Ax = b with 2 -1 1] A = |1 1 2,x = |y| and b = |b2 [-1 5 4] a. Determine if the columns of the matrix A span R³. Give your arguments. b. If the system is homogeneous, describe the trivial solution of the system (if any) in parametric vector form. Also, give a geometric description of the solution set. Give the clear argument. c. If the system is nonhomogeneous and consistent, describe b in parametric vector form. Give the clear argument. d. If b, = 5, b2 = -3, bz = 0, is the system consistent? Give valid argument. Find the solution set of the system. Compare the solution set with the trivial solution of the homogeneous system in b.
solve both (a) and (b)
Solve a simple system: 3x + 2y − z = 2x − y + 5z = −22x + y = 3 a. Matrix representation of system linear equation above into a matrix representation in form of Ax = B then find x= = A−1B, which represents x = [x y z] b. Cramer’s rule method to find x, y, and z.
x +y = 3z = 2 1) Solve the system of linear equations using the inverse matrix (2x + 3y + z = 0 3x + 4y -z = 1 A-¹ = ~3 -2 -4 2 -3 -6 6 13 BERBER 2 -3 -2 -4 -3 -6 13 6 X Z 21 ON 0 0 01 0 01
(c) Consider the system 2х1 — бх, — Хз — 38 — Зх1 — х2 + 7Хз :-34 -8x1 + x2 – 2x3 = -20 (i) Write the system in AX = B. 1 0 | and 23/10 1. (ii) Given the decomposition of matrix A is L= -3/2 -4 -6 -1 -43 b -11 -5 a 1 U = (0 -10 and the Al: 11/2 -373/20, -62 373 -11 C -20/ Find a, b and c.

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A. SOLUTION OF NON-HOMOGENEOUS SYSTEM GIVEN: 7 - 3 4 0 -7] A 2 1 -1 4 6 0 1 0 -3 -5 1. SOLVE THE SYSTEM USING GAUSSIAN ELIMINATION 1.1 TRANSFORM TO UPPER TRIANGULAR MATRIX. =