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.

(A) 4
(B) 5
(C) 9
(D) 10

Answer 1

$$\begin{array}{l} \left( \begin{array}{ccc} 1 & 2 & 3 \\ 3 & -1 & 2 \\ 4 & -6 & -4 \end{array} \right) = \begin{array}{c} 5 \\ 8 \\ -2 \end{array} \\ \left( \begin{array}{rrr} 1 & 2 & 3 \\ 0 & -7 & -7 \\ 0 & -14 & -16 \end{array} \right) = \begin{array}{c} 5 \\ -7 \\ -22 \end{array} \\ \left( \begin{array}{rrr} 1 & 2 & 3 \\ 0 & 1 & 1 \\ 0 & -14 & -16 \end{array} \right) = \begin{array}{c} 5 \\ 1 \\ -22 \end{array} \\ \left( \begin{array}{rrr} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & -2 \end{array} \right) = \begin{array}{c} 3 \\ 1 \\ -8 \end{array} \\ \left( \begin{array}{rrr} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{array} \right) = \begin{array}{c} 3 \\ 1 \\ 4 \end{array} \\ \left( \begin{array}{rrr} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right) = \begin{array}{c} -1 \\ -3 \\ 4 \end{array} \\ a = -1, b = -3, c = 4 \\ \text{Answer: (A) 4} \\ \end{array}$$