Solve the following system of linear equations: 5x1-10x2+5x3 = -20 x₁+3x2-9x3 = 16 -2x1+6x2-6x3 16
Solve the following system of linear equations: 5x1-10x2+5x3 = -20 x₁+3x2-9x3 = 16 -2x1+6x2-6x3 16
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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Question
Transcribed Image Text:Solve the following system of linear equations:
5x1-10x2+5x3
= -20
x1+3x29x3 = 16
16
-2x₁+6x₂-6x3
=
If the system has no solution, demonstrate this by giving a row-echelon form of the augmented matrix for the system.
If the system has infinitely many solutions, select "The system has at least one solution". Your answer may use expressions involving the parameters 1,
s, and t.
You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrix.
The system has no solutions
The system has no solutions
The system has at least one solution
Row-echeion form of augmented matrix:
000
000
0 0 10
Expert Solution
Step 1: Definition
Let Ax=b be a system of linear equations, then
(*) If rank(A|b)=rank(A) , then system is consistent and
- If If rank(A|b)=rank(A) = number of unknowns, Then system has unique solution.
- If If rank(A|b)=rank(A) < number of unknowns, Then the system has infinitely many solutions.
(**) If If rank(A|b)≠rank(A) , then system is inconsistent and has no solution.
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