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System of Linear Equations - Gaussian Jordan

\begin{bmatrix} 100 & -30.042 & 28.9671 \\ 28.9671 & -46.7645 & -22.2847 \\ 23.8545 & -49.8314 & 35.0697 \end{bmatrix} ⋅ X = \begin{bmatrix} 21.5967\\ -40.6101\\ 46.1507\end{bmatrix}

Perform pivoting.

a:

\begin{bmatrix} 110 & -36.124 & 25.1679 \\ 25.1679 & -43.4355 & -18.4732 \\ 27.5845 & -55.3841 & 40.6097 \end{bmatrix} ⋅ X = \begin{bmatrix} 25.9571\\ -34.0311\\ 49.0107\end{bmatrix}

Explanation

Explanation

b:

\begin{bmatrix} 90 & -33.521 & 22.7101 \\ 22.7101 & -49.5612 & -25.3127 \\ 18.4235 & -52.5284 & 31.8007 \end{bmatrix} ⋅ X = \begin{bmatrix} 27.3657\\ -33.1901\\ 41.1071\end{bmatrix}

Explanation

Explanation

c:

\begin{bmatrix} 100 & -30.042 & 28.9671 \\ 28.9671 & -46.7645 & -22.2847 \\ 23.8545 & -49.8314 & 35.0697 \end{bmatrix} ⋅ X = \begin{bmatrix} 21.5967\\ -40.6101\\ 46.1507\end{bmatrix}

Explanation

Explanation

d:

\begin{bmatrix} 113 & -32.1402 & 21.7271 \\ 21.7271 & -43.4385 & -16.4127 \\ 29.1585 & -43.3415 & 38.1097 \end{bmatrix} ⋅ X = \begin{bmatrix} 17.7712\\ -36.0174\\ 41.3107\end{bmatrix}

Explanation

Explanation

\begin{bmatrix} 100 & -30.042 & 28.9671 \\ 28.9671 & -46.7645 & -22.2847 \\ 23.8545 & -49.8314 & 35.0697 \end{bmatrix} ⋅ X = \begin{bmatrix} 21.5967\\ -40.6101\\ 46.1507\end{bmatrix}

Form the upper triangular matrix.

a:

\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} ⋅ X = \begin{bmatrix} -0.2107 \\ 0.0358 \\ 1.5103 \end{bmatrix}

Explanation

Explanation

b:

\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} ⋅ X = \begin{bmatrix} -1.1207 \\ 1.0238 \\ 1.0513 \end{bmatrix}

Explanation

Explanation

c:

\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} ⋅ X = \begin{bmatrix} -1.7021 \\ 0.8903 \\ 1.0253 \end{bmatrix}

Explanation

Explanation

d:

\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} ⋅ X = \begin{bmatrix} -0.4227 \\ 0.0874 \\ 0.0368 \end{bmatrix}

Explanation

Explanation