Consider the system of linear equations …x + y + 2z = 0 3x … ay + 5z = 1 2x … 2y … az = 7 Let S₁ be the set of all a…R for which the system is inconsistent and S₂ be the set of all a…R for which the system has infinitely many solutions. If n(S₁) and n(S₂) denote the number of elements in S₁ and S₂ respectively, then

Option C. …\Delta = \left| {\matrix{ { - 1} & 1 & 2 \cr 3 & { - a} & 5 \cr 2 & { - 2} & { - a} \cr

Matrices and Determinants

JEE Main 2021 · 1 Sep, Evening shift · Q4601

MathematicsMedium244×since 2002Q4601

Consider the system of linear equations

-

x + y + 2z = 0 3x

-

ay + 5z = 1 2x

-

-

az = 7 Let S₁ be the set of all a

\in

R for which the system is inconsistent and S₂ be the set of all a

\in

R for which the system has infinitely many solutions. If n(S₁) and n(S₂) denote the number of elements in S₁ and S₂ respectively, then

Matrices and Determinants — JEE Main 2021 · 1 Sep, Evening shift · Q4601 · Alror