- #1

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x1 + x2 + x3 [] = 2

2x1 [] + 2x3 + 2x4 = 2

x1 + 2x2 + 2x3 [] = 1

2x1 + 2x2 [] + x4 = 2

[] signify a blank space in the equation. How do you even proceed to do this, I have never seen it. Any help would be appreciated. Thank you.

- Thread starter niteshadw
- Start date

- #1

- 20

- 0

x1 + x2 + x3 [] = 2

2x1 [] + 2x3 + 2x4 = 2

x1 + 2x2 + 2x3 [] = 1

2x1 + 2x2 [] + x4 = 2

[] signify a blank space in the equation. How do you even proceed to do this, I have never seen it. Any help would be appreciated. Thank you.

- #2

TD

Homework Helper

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[tex]\left( {\begin{array}{*{20}c}

1 & 1 & 1 & 0 & 2 \\

2 & 0 & 2 & 2 & 2 \\

1 & 2 & 2 & 0 & 1 \\

2 & 2 & 0 & 1 & 2 \\

\end{array}} \right)[/tex]

Do you know how Gaussian elimination works?

- #3

saltydog

Science Advisor

Homework Helper

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How about this:

[tex]\left(

\begin{array}{cccc|c}1 & 1 & 1 & 0 & 2\\

2 & 0 & 2 & 2 & 2 \\

1 & 2 & 2 & 0 & 2 \\

2 & 2 & 0 & 1 & 1

\end{array}\right)

[/tex]

That's the augumented matrix Niteshadw.

So, reduce it. Here, I'll do the first part. I'll multiply the top row by -2 and then add it to the second row yielding:

[tex]

\left(

\begin{array}{cccc|c}1 & 1 & 1 & 0 & 2 \\

0 & -2 & 0 & 2 & -2 \\

1 & 2 & 2 & 0 & 2 \\

2 & 2 & 0 & 1 & 1

\end{array}\right)

[/tex]

Can you continue doing this until you get it to row-reduced form?

[tex]\left(

\begin{array}{cccc|c}1 & 1 & 1 & 0 & 2\\

2 & 0 & 2 & 2 & 2 \\

1 & 2 & 2 & 0 & 2 \\

2 & 2 & 0 & 1 & 1

\end{array}\right)

[/tex]

That's the augumented matrix Niteshadw.

So, reduce it. Here, I'll do the first part. I'll multiply the top row by -2 and then add it to the second row yielding:

[tex]

\left(

\begin{array}{cccc|c}1 & 1 & 1 & 0 & 2 \\

0 & -2 & 0 & 2 & -2 \\

1 & 2 & 2 & 0 & 2 \\

2 & 2 & 0 & 1 & 1

\end{array}\right)

[/tex]

Can you continue doing this until you get it to row-reduced form?

Last edited:

- #4

HallsofIvy

Science Advisor

Homework Helper

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[tex]\left(\begin{array}{cccc|c}1 & 1 & 1 & 0 & 2\\ 2 & 0 & 2 & 2 & 2 \\ 1 & 2 & 2 & 0 & 1 \\ 2 & 2 & 0 & 1 & 2 \end{array}\right)[/tex]

Except for separating out the "augmenting" part, that's just what TD said.

- #5

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Hmm..looks simple enough, just did not know what to do with those blank spots...Ok, I got this,saltydog said:How about this:

[tex]\left(

\begin{array}{cccc|c}1 & 1 & 1 & 0 & 2\\

2 & 0 & 2 & 2 & 2 \\

1 & 2 & 2 & 0 & 2 \\

2 & 2 & 0 & 1 & 1

\end{array}\right)

[/tex]

That's the augumented matrix Stunner.

So, reduce it. Here, I'll do the first part. I'll multiply the top row by -2 and then add it to the second row yielding:

[tex]

\left(

\begin{array}{cccc|c}1 & 1 & 1 & 0 & 2 \\

0 & -2 & 0 & 2 & -2 \\

1 & 2 & 2 & 0 & 2 \\

2 & 2 & 0 & 1 & 1

\end{array}\right)

[/tex]

Can you continue doing this until you get it to row-reduced form?

[tex]\left(

\begin{array}{cccc|c}1 & 0 & 0 & 0 & 3\\

0 & 1 & 0 & 0 & -1 \\

0 & 0 & 1 & 0 & 0 \\

0 & 0 & 0 & 1 & -2

\end{array}\right)

[/tex]

so um,

x_4 = -2x_4

x_3 = 0

x_2 = -x_2

x_1 = 3x_1

are those the solutions?

Thank you for the help thus far...

- #6

TD

Homework Helper

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[tex]\left\{ \begin{array}{l}

x_1 = 3 \\

x_2 = - 1 \\

x_3 = 0 \\

x_4 = - 2 \\

\end{array} \right[/tex]

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