Question

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

(A) 3
(B) 1
(C) 5
(D) 7

Answer 1

Solve the set of linear equations by the matrix method, find c.

$$\left\{ \begin{array}{l} a + 3 b + 2 c = 3 \\ 2 a - b - 3 c = - 8 \\ 5 a + 2 b + c = 9 \end{array} \right.$$ $$A = \left( \begin{array}{ccc} 1 & 3 & 2 \\ 2 & -1 & -3 \\ 5 & 2 & 1 \end{array} \right)$$ $$C = \left( \begin{array}{c} 3 \\ -8 \\ 9 \end{array} \right)$$

Solution to the system of equations is given by: $X = A^{-1}C$

The inverse of $A$ to be:

$$A^{-1} = \left( \begin{array}{ccc} -0.179 & -0.04 & 0.25 \\ 0.61 & 0.32 & -0.25 \\ -0.32 & -0.46 & 0.25 \end{array} \right)$$

Multiplying $A^{-1}$ on C we get C

$$X = \left( \begin{array}{c} 2 \\ -3 \\ 5 \end{array} \right)$$

So $a = 2$, $b = -3$, $c = 5$

Answer: (C) 5