Question:

For infinitely many solution (1) $\Delta$ = 0 | 1$5 -1$| | | 4$3 -3 = 0$| | | 24 1$\lambda$| $\Rightarrow$ 1(3$\lambda$+$3) - 5($4$\lambda$+$72) - 1(4 - 72) = 0$$\Rightarrow$ -17$\lambda$+$3 - 4$$\times$$72 - 4 = 0$$\Rightarrow$ 17$\lambda$= -289 $\Delta$$1 = 0$| 1$5 -1$| | | $\Rightarrow$ 7$3 -3 = 0$| | |$\mu$$1 -17$| $\Rightarrow$$1(-51 + 3) - 5(-119 + 3$$\mu$$) - 1(7 - 3$$\mu$$) = 0$$\Rightarrow$ -$48 + 595 - 15$$\mu$ -$7 + 3$$\mu$ = 0 $\Rightarrow$ 12$\mu$ = 540$x + 5y - z = 1$$4x + 3y - 3z = 7$$24x + y - 17z = 45$Let$z = 1$$x + 5y = 1$+$\lambda$] $\times$ 4$4x + 3y = 7$+ 3$\lambda$$4x + 20y = 4$+ 4$\lambda$-$17y = 3$-$\lambda$-17$\lambda$- 3 5$\lambda$- 15 y = ,$x = 1$+$\lambda$- 17 17$32 - 1$2$\lambda$= 17$\lambda$- 3$32 + 1$2$\lambda$7$\le$+ +$\lambda$$\le$77 17 17 30$\lambda$+ 29 7$\le$$\le$77 17 3$\le$$\lambda$$\le$42$\lambda$= 3, 20, 37 <div class="key-concept"><strong>Key Concept:</strong> Use the standard setup for consistency of linear system and simplify the resulting algebraic condition.</div> <div class="trap-box"><strong>Trap:</strong> Do not ignore the condition stated$i_n$the question while simplifying the algebra.</div>