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I have the following augmented matrix, which I assembled from a system of linear equations.

I want to reduce matrix to row-echelon form

$$ \left[\begin{array}{rrr|r} 1 & \lambda & -1 & 1\\ 2 & 1 & 2 & 5\lambda + 1 \\ 1 & -1 & 3 & 4\lambda\\ 1 & -2\lambda & 7 & 10\lambda - 1 \end{array}\right]$$

How should I go about reducing this matrix?


My attempts have yielded matrices such as:

$$ \left[\begin{array}{rrr|r} 1 & -1 & 3 & 4\lambda\\ 0 & -1 & -4 & 1-3\lambda \\ 0 & \lambda & -8 & 2- 7\lambda\\ 0 & 0 & -8 & 4-5\lambda \end{array}\right]$$

And

$$ \left[\begin{array}{rrr|r} 1 & \lambda & -1 & 1\\ 0 & 3 & -4 & 1-3\lambda \\ 1 & 0 & -9 & 3- 5\lambda\\ 0 & 0 & 32 & 25\lambda - 8 \end{array}\right]$$

But I couldn't zero out one of the rows.

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  • $\begingroup$ Subtract the first row from the third? $\endgroup$ – John Doe May 3 '17 at 15:17
  • $\begingroup$ @JohnDoe The first matrix or the second? $\endgroup$ – Cobbles May 3 '17 at 15:20
  • $\begingroup$ The second one, so that the 1 in the $(3,1)$ entry gets cancelled out. Is this what you're trying to do? $\endgroup$ – John Doe May 3 '17 at 15:21
  • $\begingroup$ @JohnDoe I am trying to use gaussian elimination to create an upper triangular matrix $\endgroup$ – Cobbles May 3 '17 at 15:22
  • $\begingroup$ And I need one of the rows to be zeroes $\endgroup$ – Cobbles May 3 '17 at 15:23

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