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\begin{bmatrix} -148.03 & -40.1285 & -30.7076 \\ 4.275 & -18.2927 & -18.1788 \\ -41.3615 & 4.9235 & 9.5546 \end{bmatrix} ⋅ X = \begin{bmatrix} -35.8497 \\ -97.2592 \\ 49.5498 \end{bmatrix}

Perform pivoting.

\begin{bmatrix} -158.73 & -30.1852 & -26.0861 \\ 5.275 & -28.2492 & -15.2268 \\ -47.1532 & 3.356 & 2.4836 \end{bmatrix} ⋅ X = \begin{bmatrix} -25.8397 \\ -87.8422 \\ 45.7358 \end{bmatrix}

Explanation

\begin{bmatrix} -136.73 & -37.1628 & -27.7607 \\ 7.727 & -12.2792 & -28.1878 \\ -39.6155 & 7.2385 & 4.5467 \end{bmatrix} ⋅ X = \begin{bmatrix} -39.4897 \\ -87.4292 \\ 43.4978 \end{bmatrix}

Explanation

\begin{bmatrix} -140.13 & -30.1345 & -34.7936 \\ 5.4227 & -12.1227 & -11.2378 \\ -48.6315 & 3.2935 & 10.4536 \end{bmatrix} ⋅ X = \begin{bmatrix} -32.9237 \\ -91.5962 \\ 46.3554 \end{bmatrix}

Explanation

\begin{bmatrix} -148.03 & -40.1285 & -30.7076 \\ 4.275 & -18.2927 & -18.1788 \\ -41.3615 & 4.9235 & 9.5546 \end{bmatrix} ⋅ X = \begin{bmatrix} -35.8497 \\ -97.2592 \\ 49.5498 \end{bmatrix}

Explanation

\begin{bmatrix} -148.03 & -40.1285 & -30.7076 \\ 4.275 & -18.2927 & -18.1788 \\ -41.3615 & 4.9235 & 9.5546 \end{bmatrix} ⋅ X = \begin{bmatrix} -35.8497 \\ -97.2592 \\ 49.5498 \end{bmatrix}

Start with initial guess solution [0 0 0]T. Perform Gauss Seidel iteration and find the 1^st 3 row of the matrix. Relaxation factor = 0.5.

\begin{bmatrix} 0.1121 & 1.8626 & 1.6165 \\ -1.5803 & 1.7087 & 3.1572 \\ -0.8641 & 2.9107 & 2.381 \end{bmatrix}

Explanation

\begin{bmatrix} 0.1211 & 2.6726 & 2.1665 \\ -0.4053 & 2.8708 & 2.0592 \\ -0.6843 & 2.9907 & 1.371 \end{bmatrix}

Explanation

\begin{bmatrix} 1.5213 & 2.7246 & 1.6359 \\ -1.3540 & 2.0188 & 1.1202 \\ -0.8743 & 2.1607 & 2.4571 \end{bmatrix}

Explanation

\begin{bmatrix} 0.1261 & 1.6521 & 1.1061 \\ -1.4270 & 2.2887 & 1.1052 \\ -0.6144 & 2.9207 & 1.519 \end{bmatrix}

Explanation

System of Linear Equations: Gaussian Seidel with relaxation Method