Linear AlgebraThe system represents a nonhomogeneous system Ax = b where b/ = 0. Consider the correspondinghomogeneous system Ax = 0. Write the solution to the homogeneous system in parametric form. It mayhelp to write the updated augmented matrix first.10-2-1-3M =11-310 0 00

Answered: The system represents a nonhomogeneous…

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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Let A and B be matrices of thesame size. If x is a solution to both the system Ax =0 and the system Bx = 0, show that x is a solution tothe system (A + B)x = 0. Provide reasoning/details please.
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)
1. 0 2 4 1 -1 10 0 0 1 1 The reduced row echelon form of the augmented matrix of a linear system is given above. Describe the solution set of this linear system in parametric vector form.
Consider the matrix below as the augmented matrix of a linear system: SKIP h -2 For which value(s) of h is the linear system corresponding to this augmented matrix consistent? Write your answer in one of the following forms: • h = ... (orh = h = ... etc.) • h+ ... (or h+ ..., h+ ... etc.) • all h • no h. (Type \neq to get the sign.)

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The system represents a nonhomogeneous system Ax = b where b/ = 0. Consider the corresponding homogeneous system Ax = 0. Write the solution to the homogeneous system in parametric form. It may help to write the updated augmented matrix first. 1 -2 -1 -3 M = 1 1 -3 1 0 0