For the following system to be consistent,\[ \begin{align*}7x - 5y + 3z &= 3 \\-53x + 31y + kz &= 6 \\8x - 4y - 8z &= -3\end{align*}\]we must have $ k \neq $ [box for input].

The given system of equation is Therefore the matrix form is AX=BWhere .Hence the augmented matrix…

Answered: For the following system to be…

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

For the following system to be consistent,

\[
\begin{align*}
7x - 5y + 3z &= 3 \\
-53x + 31y + kz &= 6 \\
8x - 4y - 8z &= -3
\end{align*}
\]

we must have $ k \neq $ [box for input].

Expert Solution

Step 1: Given system of equation:

The given system of equation is

$7 x minus 5 y plus 3 z equals 3 minus 53 x plus 31 y plus k z equals 6 8 x minus 4 y minus 8 z equals negative 3$

Therefore the matrix form is AX=B

Where $A equals open square brackets table row 7 cell negative 5 end cell 3 row cell negative 53 end cell 31 k row 8 cell negative 4 end cell cell negative 8 end cell end table close square brackets comma X equals open square brackets table row x row y row z end table close square brackets comma B equals open square brackets table row 3 row 6 row cell negative 3 end cell end table close square brackets$ .

Hence the augmented matrix is

$left square bracket A colon B right square bracket equals open square brackets table row 7 cell negative 5 end cell 3 vertical line 3 row cell negative 53 end cell 31 k vertical line 6 row 8 cell negative 4 end cell cell negative 8 end cell vertical line cell negative 3 end cell end table close square brackets$