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\begin{bmatrix} 185.4236 & -31.4161 & -30.6022 \\ 17.4439 & -10.0438 & -47.5348 \\ 25.5032 & -5.8169 & 2.5353 \end{bmatrix} ⋅ X = \begin{bmatrix} 19.1544\\ -21.5367\\ 6.5871 \end{bmatrix}

Perform pivoting

\begin{bmatrix} 175.3126 & 39.6671 & -28.1602 \\ -27.3249 & 18.1481 & -37.7458 \\ 20.3202 & -6.1649 & 2.5353 \end{bmatrix} ⋅ X = \begin{bmatrix} -14.4144\\ 22.3647\\ -4.7152 \end{bmatrix}

Explanation

\begin{bmatrix} 185.4236 & -31.4161 & -30.6022 \\ 17.4439 & -10.0438 & -47.5348 \\ 25.5032 & -5.8169 & 2.5353 \end{bmatrix} ⋅ X = \begin{bmatrix} 19.1544\\ -21.5367\\ 6.5871 \end{bmatrix}

Explanation

\begin{bmatrix} -167.34126 & 9.6211 & -20.1622 \\ -17.4239 & -7.3821 & 37.548 \\ -15.1532 & 8.1619 & 3.4553 \end{bmatrix} ⋅ X = \begin{bmatrix} -29.5414\\ -29.1257\\ -6.9171 \end{bmatrix}

Explanation

\begin{bmatrix} 173.3416 & -36.1651 & 33.6222 \\ -14.1439 & 14.5048 & -57.2548 \\ -15.0342 & 5.8691 & -2.5532 \end{bmatrix} ⋅ X = \begin{bmatrix} 39.4754\\ 25.5127\\ -6.5621 \end{bmatrix}

Explanation

\begin{bmatrix} 185.4236 & -31.4161 & -30.6022 \\ 17.4439 & -10.0438 & -47.5348 \\ 25.5032 & -5.8169 & 2.5353 \end{bmatrix} ⋅ X = \begin{bmatrix} 19.1544\\ -21.5367\\ 6.5871 \end{bmatrix}

Start with initial guess solution [0 0 0]T. Perform Gauss Seidel iteration and find the 1st 3 row of the matrix.

\begin{bmatrix} 0.1033 & 2.3237 & 6.8904 \\ 1.6342 & -27.6281 & -77.2295 \\ -17.3236 & 337.5648 & 951.3568 \end{bmatrix}

Explanation

\begin{bmatrix} 1.0241 & 3.1327 & -4.0524 \\ 2.4262 & -21.4561 & 72.2595 \\ 15.3684 & -236.748 & 653.5368 \end{bmatrix}

Explanation

\begin{bmatrix} 0.3343 & 1.3784 & 7.9034 \\ 2.5372 & -37.8681 & -71.2755 \\ -12.1364 & 327.4368 & 781.5868 \end{bmatrix}

Explanation

\begin{bmatrix} 1.0113 & 1.3217 & 5.9074 \\ 2.1624 & -24.8621 & -71.2795 \\ -12.1336 & 367.5498 & 872.5278 \end{bmatrix}

Explanation

System of Linear Equations - Gaussian Seidel