Question

Use Gaussian elimination method to solve the following equation.
2x-3y+2z=6
x+4y-3z=12
3x-5y+2z=8

Answer 1

Answer on Question #78887 - Math - Linear Algebra

Use Gaussian elimination method to solve the following equation.

$$2x - 3y + 2z = 6$$ $$x + 4y - 3z = 12$$ $$3x - 5y + 2z = 8$$

Solution.

$$\begin{bmatrix} 2 & -3 & 2 & 6 \\ 1 & 4 & -3 & 12 \\ 3 & -5 & 2 & 8 \end{bmatrix} \rightarrow$$

subtract row1 from row3

$$\rightarrow \begin{bmatrix} 2 & -3 & 2 & 6 \\ 1 & 4 & -3 & 12 \\ 1 & -2 & 0 & 2 \end{bmatrix} \rightarrow$$

multiply row2 by 2 & add to row2 3*row1

$$\rightarrow \begin{bmatrix} 2 & -3 & 2 & 6 \\ 8 & -1 & 0 & 42 \\ 1 & -2 & 0 & 2 \end{bmatrix} \rightarrow$$

subtract from row2 8*row3 & divide row2 by 15 & add to row3 2*row2

$$\rightarrow \begin{bmatrix} 2 & -3 & 2 & 6 \\ 0 & 1 & 0 & \frac{26}{15} \\ 1 & 0 & 0 & \frac{82}{15} \end{bmatrix} \rightarrow$$

subtract from row1 2*row3 & add to row1 3*row2 & divide row1 by 2

$$\rightarrow \begin{bmatrix} 0 & 0 & 1 & \frac{2}{15} \\ 0 & 1 & 0 & \frac{26}{15} \\ 1 & 0 & 0 & \frac{82}{15} \end{bmatrix}$$

Answer: $x = \frac{82}{15}, y = \frac{26}{15}, z = \frac{2}{15}$

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