Virtual Labs

\begin{bmatrix} 100 & 13.9869 & 26.5369 \\ 26.5369 & -33.1709 & -29.7082 \\ 48.772 & -23.465 & 35.839 \end{bmatrix} ⋅ X = \begin{bmatrix} 67.3986\\ 69.4181\\ 7.1902 \end{bmatrix}

Perform pivoting.

\begin{bmatrix} 110 & 1.6219 & 16.1289 \\ 24.5619 & -30.0129 & -25.8212 \\ 41.-572 & 13.345 & -32.189 \end{bmatrix} ⋅ X = \begin{bmatrix} -61.1386\\ 64.3461\\ 6.9213 \end{bmatrix}

Explanation

\begin{bmatrix} 114 & -15.9162 & 29.6931 \\ 27.6359 & 31.0319 & -21.1022 \\ 44.221 & 27.645 & 29.389 \end{bmatrix} ⋅ X = \begin{bmatrix} 74.0136\\ 74.1281\\ -4.6702 \end{bmatrix}

Explanation

\begin{bmatrix} 100 & 13.9869 & 26.5369 \\ 26.5369 & -33.1709 & -29.7082 \\ 48.772 & -23.465 & 35.839 \end{bmatrix} ⋅ X = \begin{bmatrix} 67.3986\\ 69.4181\\ 7.1902 \end{bmatrix}

Explanation

\begin{bmatrix} -107 & -16.0461 & 17.2149 \\ 26.5369 & -33.1709 & -29.0172 \\ 14.2013 & -14.5721 & -27.631 \end{bmatrix} ⋅ X = \begin{bmatrix} -57.3216\\ 52.4115\\ 10.1021 \end{bmatrix}

Explanation

\begin{bmatrix} 100 & 13.9869 & 26.5369 \\ 26.5369 & -33.1709 & -29.7082 \\ 48.772 & -23.465 & 35.839 \end{bmatrix} ⋅ X = \begin{bmatrix} 67.3986\\ 69.4181\\ 7.1902 \end{bmatrix}

Take the tolerance as 10-6. Start with initial huess solution [0 0 0]T. Perform Jacobi iteration and find X.

\begin{bmatrix} 1.4716 \\ -1.0183 \\ -2.4685 \end{bmatrix}

Explanation

\begin{bmatrix} -1.3116 \\ 1.5033 \\ -3.8675 \end{bmatrix}

Explanation

\begin{bmatrix} 2.1316 \\ 1.3873 \\ -2.7214 \end{bmatrix}

Explanation

\begin{bmatrix} 1.0136 \\ -1.3481 \\ -1.8345 \end{bmatrix}

Explanation

System of Linear Equations: Jacobi Method