Consider the homogeneous system of equations 4x1 +10x2 +6x3 −4x5 =0 2x1 +5x2 +3x3 +6x4 +4x5 = 0 x1 +2x2 +x3 +3x4 +x5 = 0. Row reduces the augmented system to reduced echelon form. Identify the free variables and basic variables  Write down the parametric solution of the system.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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I'm encountering difficulties in solving this problem using only matrix notation, and I'm seeking your guidance. The requirement is to solve it solely using matrix notation, without any alternative approaches. Could you please provide a detailed, step-by-step explanation using matrix notation to help me reach the final solution?

 

The problem requires solving it solely through the matrix approach, without using any other methods. Could you please provide a comprehensive, step-by-step explanation that will guide me towards the solution? This will help me grasp the process thoroughly and follow it accurately.

you cannot reverse this you can do R3-R4 to R4->R3 you cannot do that.

question:

Consider the homogeneous system of equations

4x1 +10x2 +6x3 −4x5 =0
2x1 +5x2 +3x3 +6x4 +4x5 = 0

x1 +2x2 +x3 +3x4 +x5 = 0.

Row reduces the augmented system to reduced echelon form.

Identify the free variables and basic variables 

Write down the parametric solution of the system.

 

 

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