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A = \begin{bmatrix} 436.6216 & -194.4377 & 0 \\ -194.4377 & 307.159 & -112.7213 \\ 0 & -112.7213 & 112.7213 \end{bmatrix}

d = \begin{bmatrix} 89.8026 \\ 48.4647 \\ 70.2897 \end{bmatrix}

A × X = d

Find vector a, b and c.

a = \begin{vmatrix} -194.4377 \\ -112.7213 \\ 0 \end{vmatrix}, \quad b = \begin{vmatrix} 307.159 \\ 112.7213\\ 436.6216 \end{vmatrix}, \quad c = \begin{vmatrix} -112.7213 \\ 0 \\ -194.4377 \end{vmatrix}

Explanation

a = \begin{vmatrix} -194.4377 \\ 0 \\ -112.7213 \end{vmatrix}, \quad b = \begin{vmatrix} 307.159 \\ 436.6216 \\ 112.7213 \end{vmatrix}, \quad c = \begin{vmatrix} -112.7213 \\ -194.4377 \\ 0 \end{vmatrix}

Explanation

a = \begin{vmatrix} -112.7213\\ 0 \\ -194.4377 \end{vmatrix}, \quad b = \begin{vmatrix} 112.7213\\ 436.6216 \\ 307.159 \end{vmatrix}, \quad c = \begin{vmatrix} 0\\ -194.4377 \\ -112.7213 \end{vmatrix}

Explanation

a = \begin{vmatrix} 0 \\ -194.4377 \\ -112.7213 \end{vmatrix}, \quad b = \begin{vmatrix} 436.6216 \\ 307.159 \\ 112.7213 \end{vmatrix}, \quad c = \begin{vmatrix} -194.4377 \\ -112.7213 \\ 0 \end{vmatrix}

Explanation

Find the updated value of a, b, c and d after performing the upper triangular matrix. Refer the a, b, c, and d values from Question 1.

a = \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}, \quad b = \begin{bmatrix} 55.116 \\ 436.6216 \\ 220.5714 \end{bmatrix}, \quad c = \begin{bmatrix} 0\\ -194.4377 \\ -112.7213 \end{bmatrix}, \quad d = \begin{bmatrix} 115.4944 \\ 89.8026 \\ 88.4559 \end{bmatrix}

Explanation

a = \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}, \quad b = \begin{bmatrix} 220.5714 \\ 55.116 \\ 436.6216 \end{bmatrix}, \quad c = \begin{bmatrix} -112.7213 \\ 0 \\ -194.4377 \end{bmatrix}, \quad d = \begin{bmatrix} 88.4559 \\ 115.4944 \\ 89.8026 \\ \end{bmatrix}

Explanation

a = \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}, \quad b = \begin{bmatrix} 436.6216 \\ 220.5714 \\ 55.116 \end{bmatrix}, \quad c =\begin{bmatrix} -194.4377 \\ -112.7213 \\ 0 \end{bmatrix}, \quad d = \begin{bmatrix} 89.8026 \\ 88.4559 \\ 115.4944 \end{bmatrix}

Explanation

a = \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}, \quad b = \begin{bmatrix} 220.5714 \\ 436.6216 \\ 55.116 \end{bmatrix}, \quad c = \begin{bmatrix} -112.7213 \\ -194.4377 \\ 0 \end{bmatrix}, \quad d = \begin{bmatrix} 88.4559 \\ 89.8026 \\ 115.4944 \end{bmatrix}

Explanation

System of Linear Equations - Thomas Alogrithm