Numerical Methods20795 marksNumerical: Gaussian eliminationGaussian elimination method
Solve the following system of linear equations using Gaussian elimination method.
Solve the following system of linear equations using Gaussian elimination method.
$$\begin{aligned} 2x + 2y + z &= 12 \ 3x + 2y + 2z &= 8 \ 5x + 10y - 8z &= 10 \end{aligned}$$
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System of equations: - $2x + 2y + z = 12$ - $3x + 2y + 2z = 8$ - $5x + 10y - 8z = 10$ Augmented matrix: $$[Ab] = \begin{bmatrix} 2 & 2 & 1 & & 12 \ 3 & 2 & 2 & & 8 \ 5 & 10 & -8 & & 10 \end{bmatrix}$$ Eliminate x from R2: $R2 \to R2 - \frac{3}{2}R1$ $$\left(3-3,\ 2-3,\ 2-\tfrac{3}{2},\ 8-18\rig...