Question

Solve the set of linear equations by Guassian elimination method : a+2b+3c=5, 3a-b+2c=8, 4a-6b-4c=-2. Find c

Answer 1

Answer on Question #40997 – Math – Linear Algebra

Question:

Solve the set of linear equations by Gaussian elimination method: $a + 2b + 3c = 5$, $3a - b + 2c = 8$, $4a - 6b - 4c = -2$. Find c

Solution:

Rewrite the system in matrix form and solve it by Gaussian Elimination

$$\left( \begin{array}{rrrr} 1 & 2 & 3 & 5 \\ 3 & -1 & 2 & 8 \\ 4 & -6 & -4 & 2 \end{array} \right)$$

from 2; 3 rows we subtract the 1-th row, multiplied respectively by 3; 4

$$\left( \begin{array}{rrrr} 1 & 2 & 3 & 5 \\ 0 & -7 & -7 & -7 \\ 0 & -14 & -16 & -18 \end{array} \right)$$

devide the 2-th row by -7

$$\left( \begin{array}{rrrr} 1 & 2 & 3 & 5 \\ 0 & 1 & 1 & 1 \\ 0 & -14 & -16 & -18 \end{array} \right)$$

from 1; 3 rows we subtract the 2-th row, multiplied respectively by 2; -14

$$\left( \begin{array}{rrrr} 1 & 0 & 1 & 3 \\ 0 & 1 & 1 & 1 \\ 0 & 0 & -2 & -4 \end{array} \right)$$

devide the 3-th row by -2

$$\left( \begin{array}{rrrr} 1 & 0 & 1 & 3 \\ 0 & 1 & 1 & 1 \\ 0 & 0 & 1 & 2 \end{array} \right)$$

from 1; 2 rows we subtract the 3-th row, multiplied respectively by 1; 1

$$\left( \begin{array}{rrrr} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & -1 \\ 0 & 0 & 1 & 2 \end{array} \right)$$

Answer:

$$\left\{ \begin{array}{l} a = 1 \\ b = -1 \\ c = 2 \end{array} \right.$$

Answer: $c = 2$