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" determine conditions on the bi's, if any, in order to guarantee that the linear system is consistent."

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

" determine conditions on the bi's, if any, in order to guarantee that the linear system is consistent."

x1 - 2x2 + 5x3
4x1 - 5x2 + 8x3
-3x₁ + 3x₂ − 3x3
b₁
b₂
b3

Expert Solution

Step 1

Given that,

The linear system of equations, We have to check whether the this system of linear equations is consistent or not.

$x_{1} - 2 x_{2} + 5 x_{3} = b_{1} 4 x_{1} - 5 x_{2} + 8 x_{3} = b_{2} - 3 x_{1} + 3 x_{2} - 3 x_{3} = b_{3}$

Therefore, first construct the matrix corresponding the given linear system. Let the matrix is $A$ .

$A = [\begin{matrix} 1 & - 2 & 5 \\ 4 & - 5 & 8 \\ - 3 & 3 & - 3 \end{matrix}]$

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