Solve the following system of linear equations using Gauss-Jordan elim | Numerical Method 2081

Numerical Method20815 marksNumerical: Gauss-Jordan elimination methodGauss-Jordan method

Solve the following system of linear equations using Gauss-Jordan elimination method:

\begin{aligned} x + 2y - 3z &= 4 \\ 2x + 4y - 6z &= 8 \\ x - 2y + 5z &= 4 \end{aligned}

[5]

Solve the following system of linear equations using Gauss-Jordan elimination method:

$$ \begin{aligned} x + 2y - 3z &= 4 \ 2x + 4y - 6z &= 8 \ x - 2y + 5z &= 4 \end{aligned} $$

[5]

System of equations: $x + 2y - 3z = 4 \quad \cdots (1)$ $2x + 4y - 6z = 8 \quad \cdots (2)$ $x - 2y + 5z = 4 \quad \cdots (3)$ $[Ab] = \begin{bmatrix} 1 & 2 & -3 & & 4 \\ 2 & 4 & -6 & & 8 \\ 1 & -2 & 5 & & 4 \end{bmatrix}$ $R2 \to R2 - 2R1$ : $[0,\ 0,\ 0,\ \ 0]$ $R3 \to R3 - R1$ :

System of equations: $$x + 2y - 3z = 4 \quad \cdots (1)$$ $$2x + 4y - 6z = 8 \quad \cdots (2)$$ $$x - 2y + 5z = 4 \quad \cdots (3)$$ $$[Ab] = \begin{bmatrix} 1 & 2 & -3 & & 4 \ 2 & 4 & -6 & & 8 \ 1 & -2 & 5 & & 4 \end{bmatrix}$$ $R2 \to R2 - 2R1$: $[0,\ 0,\ 0,\ \ 0]$ $R3 \to R3 - R1$:

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