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)

$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