Question

Solve the matrix!

Answer 1

how can i eliminate B from the 1st collumn?

Answer 2

where A B and C are constants

Answer 3

...and V

Answer 4

Is this the matrix?
\[
\begin{bmatrix}
0&0&A&1&V\\
0&1&0&1&0\\
A&1&0&0&0\\
B&0&C&0&0
\end{bmatrix}
\]

Answer 5

yes!

Answer 6

Does A=0?

Answer 7

no

Answer 8

please swap the first row with the third row first
\[\left( {\begin{array}{*{20}{c}}
A&1&0&0 \\
0&1&0&1 \\
0&0&A&1 \\
B&0&C&0
\end{array}\quad \begin{array}{*{20}{c}}
0 \\
0 \\
V \\
0
\end{array}} \right)\]

Answer 9

A is equal to some positive distance divided by 2 and B and C are equal to some viscosities

Answer 10

Are all constants not equal to 0?

Answer 11

Are they known constants or unknown constants?

Answer 12

then replace the fourth row with this row:
\[\left( {B\;0\;C\;0\;0} \right) - \frac{B}{A}\left( {A\;1\;0\;0\;0} \right) = ...?\]

Answer 13

they are unknown constants

Answer 14

Just do Gaussian elimination. Nothing special but cumbersome.

Answer 15

I'm not sure how to eliminate the constants. If I could see an example I could probably understand it for future use.

Answer 16

\[\left( {B\;0\;C\;0\;0} \right) - \frac{B}{A}\left( {A\;1\;0\;0\;0} \right) = \left( {0\; - \frac{B}{A}\;C\;0\;0} \right)\quad \]

Answer 17

As the constants are not equal to zero, just multiply the whole row by the inverse of that constant.

Answer 18

Oh, I see. Could you do a little more so I can get the hang of it. Thank you Michele_Laino

Answer 19

@Michele_Laino

Answer 20

For example:
\[
\frac{1}{A}
\begin{bmatrix}
A&1&0&0&0
\end{bmatrix}
=
\begin{bmatrix}
1&\frac{1}{A}&0&0&0
\end{bmatrix}
\]

Answer 21

your Matrix at the first step of the Gaussian method will be this:
\[\left( {\begin{array}{*{20}{c}}
A&1&0&0 \\
0&1&0&1 \\
0&0&A&1 \\
0&{ - \frac{B}{A}}&C&0
\end{array}\quad \begin{array}{*{20}{c}}
0 \\
0 \\
V \\
0
\end{array}} \right)\]

Answer 22

\[
\begin{bmatrix}
1&\frac{1}{A}&0&0&0\\
0&1&0&1&0\\
0&0&A&1&V\\
B&0&C&0&0
\end{bmatrix}
\\
R_4-BR_1
\\
\begin{bmatrix}
1&\frac{1}{A}&0&0&0\\
0&1&0&1&0\\
0&0&A&1&V\\
0&-\frac{B}{A}&C&0&0
\end{bmatrix}
\]

Answer 23

Thank you both I understand now!

Answer 24

Thank you! :) @znimon