Question

Consider the system of linear equations; $x_1 + 2x_2 + x_3 = 3$ $2x_1 + 3x_2 + x_3 = 3$ $3x_1 + 5x_2 + 2x_3 = 1$ The system has

• A. exactly 3 solutions
• B. a unique solution
• C. no solution
• D. infinite number of solutions

Answer 1

Answer: (C)

no solution

Answer 2

$D = \begin{vmatrix}1&2&1\\\ 2&3&1\\\ 3&5&2\end{vmatrix} = 0$ $D_{1} = \begin{vmatrix}3&2&1\\\ 3&3&1\\\ 1&5&2\end{vmatrix}\ne0$ $\Rightarrow$ Given system, does not have any solution. $\Rightarrow$ No solution