\begin{equation*} \begin{bmatrix} 4 & -1 & -1 & 0 &|&30 \\ -1 & 4 & 0 & -1&|&60 \\ -1 & 0 & 4 & -1&|&40 \\ 0 & -1 & -1 & 4&|&70 \end{bmatrix} \end{equation*}
What's the best way to solve the matrix above? There's a clear pattern of the diagonal 4's and 0's and the -1's so I feel like there has to be a better way of doing things rather than using scaling and row reduction.
If I do those methods I end up with messy fractions.
My Step 1:
New Row 2 = (1/4)Row 1 + Row 2
Even at step 1 I can tell the whole thing will be messy with fractions.
Is there a better way to solve this matrix? Or am I doing it wrong? Thanks.