Question

Solve the set of linear equations by the matrix method : a+3b+2c=3 , 2a-b-3c= -8, 5a+2b+c=9. Sove for b.

(A) 9
(B) -3
(C) 5
(D) -4

Answer 1

$$\begin{array}{l} \left( \begin{array}{ccc} 1 & 3 & 2 \\ 2 & -1 & -3 \\ 5 & 2 & 1 \end{array} \right) = \left( \begin{array}{c} 3 \\ -8 \\ 9 \end{array} \right) \\ \left( \begin{array}{ccc} 1 & 3 & 2 \\ 0 & 1 & 1 \\ 0 & -13 & -9 \end{array} \right) = \left( \begin{array}{c} 3 \\ 2 \\ -6 \end{array} \right) \\ \left( \begin{array}{ccc} 1 & 0 & -1 \\ 0 & 1 & 1 \\ 0 & 0 & 4 \end{array} \right) = \left( \begin{array}{c} -3 \\ 2 \\ 20 \end{array} \right) \\ \left( \begin{array}{ccc} 1 & 0 & -1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{array} \right) = \left( \begin{array}{c} -3 \\ 2 \\ 5 \end{array} \right) \\ \left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right) = \left( \begin{array}{c} 2 \\ -3 \\ 5 \end{array} \right) \end{array}$$ $$a = 2, b = -3, c = 5$$

Answer: (B) -3