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 #59715 – 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

$$\left\{ \begin{array}{l l} a + 2b + 3c = 5 \\ 3a - b + 2c = 8 \\ 4a - 6b - 4c = -2 \end{array} \right.$$

the second equation minus the first equation multiplied by $3 \rightarrow$

$$\left\{ \begin{array}{l l} a + 2b + 3c = 5 \\ -7b - 7c = -7 \\ 4a - 6b - 4c = -2 \end{array} \right.$$

the third equation minus the first equation multiplied by $4 \rightarrow$

$$\left\{ \begin{array}{l l} a + 2b + 3c = 5 \\ -7b - 7c = -7 \\ -14b - 16c = -22 \end{array} \right.$$

the third equation minus the second equation multiplied by $2 \rightarrow$

$$\left\{ \begin{array}{c} a + 2b + 3c = 5 \\ -7b - 7c = -7 \\ -2c = -8 \end{array} \right.$$

divide the second equation by (-7) and the third one by $(-2) \rightarrow$

$$\left\{ \begin{array}{c} a + 2b + 3c = 5 \\ b + c = 1 \\ c = 4 \end{array} \right.$$

So,

$$c = 4,$$ $$b = 1 - c = 1 - 4 = -3,$$ $$a = 5 - 2b - 3c = 5 - 2 \cdot (-3) - 3 \cdot 4 = -1.$$

Answer: $c = 4$.

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