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Consider the following system of equations: x+2y-3z=a 2x+6y-11z=b x-2y-7z=c where a,b and c are real constants. Then the system of equations :
Option: 1 has no solution for all a,b and c.
Option: 2 has a unque solution when 5a = 2b+c
Option: 3 has unique solution for all a,b and c
Option: 4 has infinite number of solutions when 5a = 2b+c

Answers (1)

best_answer

\begin{aligned} &P_{1}: x+2 y-3 z=a\\ &P_{2}: 2 x+6 y-11 z=b\\ &P_{3}: x-2 y+7 z=c\\ &\text { Clearly }\\ &5 \mathrm{P}_{1}=2 \mathrm{P}_{2}+\mathrm{P}_{3} \quad \text { if } 5 \mathrm{a}=2 \mathrm{~b}+\mathrm{c} \end{aligned}

⇒ All the planes sharing a line of intersection

⇒ infinite solutions

Posted by

himanshu.meshram

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