Determinants
General
Grade 12
Question:
Find the nature of solution for the given system of equations:<br>$x + 2y + 3z = 1; 2x + 3y + 4z = 3; 3x + 4y + 5z = 0$
Step-by-Step Solution
Key Concept: General
$$D = \begin{vmatrix} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 3 & 4 & 5 \end{vmatrix} = 0$$<br>Now, $D_1 = \begin{vmatrix} 1 & 2 & 3 \\ 3 & 3 & 4 \\ 0 & 4 & 5 \end{vmatrix} = 5$<br>$\because D = 0$ but $D_1 \neq 0$<br>Hence no solution.
Correct Answer: D