Consider the matrix below that represents a homogeneous system, and has been reduced: ### Matrix System AnalysisConsider the following augmented matrix:\[\begin{pmatrix}1 & 0 & 8 & \vert & 10 \\0 & 1 & 0 & \vert & 0 \\0 & A & B & \vert & b \\\end{pmatrix}\]This matrix corresponds to a system of linear equations involving variables \( x \), \( y \), and \( z \).**Tasks:**(a) **Explain** specific values of \( A \) and \( B \) such that the corresponding system of equations has one unique solution. If no such values can be found, **explain** why not.(b) **Explain** specific values of \( A \) and \( B \) such that the corresponding system of equations has infinitely many solutions. If no such values can be found, **explain** why not.(c) **Explain** specific values of \( A \) and \( B \) such that the corresponding system of equations has no solution. If no such values can be found, **explain** why not.### Problem ExplanationTo determine what specific combinations of \( A \) and \( B \) lead to different types of solutions, we need to consider the conditions that affect the rank of the matrix and the implications for consistency and the number of solutions:- **Unique Solution:** For a unique solution, the system must be consistent and the rank of the matrix must equal the number of variables. - **Infinitely Many Solutions:** The system is consistent, but the rank of the matrix is less than the number of variables, or there are free variables.- **No Solution:** The system is inconsistent, indicated by a contradictory equation such as 0 = b where b is a non-zero constant.Understanding these principles will guide you in assigning values to \( A \) and \( B \) to obtain the specified outcomes.

Given matrix in reduced form is 108:0010:00AB:0 for the system AX=bwhere X=xyz,b=000

108 : 0 0 1 0 A B : 0 : 0 x y z : b (a): Explain specific values of A and B such that the corresponding system of equations has one unique solution. If no such values can be found, explain why not. (b): Explain specific values of A and B such that the corresponding system of equations has infinitely many solutions. If no such values can be found, explain why not. (c): Explain specific values of A and B such that the corresponding system of equations has no solution. If no such values can be found, explain why not.

108 : 0 0 1 0 A B : 0 : 0 x y z : b (a): Explain specific values of A and B such that the corresponding system of equations has one unique solution. If no such values can be found, explain why not. (b): Explain specific values of A and B such that the corresponding system of equations has infinitely many solutions. If no such values can be found, explain why not. (c): Explain specific values of A and B such that the corresponding system of equations has no solution. If no such values can be found, explain why not.

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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