jee-main 2020 Q63

jee-main · India · session2_05sep_shift1 3x3 Matrices Linear System Existence and Uniqueness via Determinant

Let $\lambda \in \mathrm { R }$. The system of linear equations $2 x _ { 1 } - 4 x _ { 2 } + \lambda x _ { 3 } = 1$ $x _ { 1 } - 6 x _ { 2 } + x _ { 3 } = 2$ $\lambda x _ { 1 } - 10 x _ { 2 } + 4 x _ { 3 } = 3$ is inconsistent for :
(1) exactly one positive value of $\lambda$
(2) exactly one negative value of $\lambda$
(3) every value of $\lambda$
(4) exactly two values of $\lambda$

Let $\lambda \in \mathrm { R }$. The system of linear equations\\
$2 x _ { 1 } - 4 x _ { 2 } + \lambda x _ { 3 } = 1$\\
$x _ { 1 } - 6 x _ { 2 } + x _ { 3 } = 2$\\
$\lambda x _ { 1 } - 10 x _ { 2 } + 4 x _ { 3 } = 3$\\
is inconsistent for :\\
(1) exactly one positive value of $\lambda$\\
(2) exactly one negative value of $\lambda$\\
(3) every value of $\lambda$\\
(4) exactly two values of $\lambda$

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