jee-main 2015 Q78

jee-main · India · 04apr 3x3 Matrices Linear System Existence and Uniqueness via Determinant

The set of all values of $\lambda$ for which the system of linear equations: $2 x _ { 1 } - 2 x _ { 2 } + x _ { 3 } = \lambda x _ { 1 }$ $2 x _ { 1 } - 3 x _ { 2 } + 2 x _ { 3 } = \lambda x _ { 2 }$ $- x _ { 1 } + 2 x _ { 2 } = \lambda x _ { 3 }$ has a non-trivial solution,
(1) Contains more than two elements.
(2) Is an empty set.
(3) Is a singleton.
(4) Contains two elements.

The set of all values of $\lambda$ for which the system of linear equations:\\
$2 x _ { 1 } - 2 x _ { 2 } + x _ { 3 } = \lambda x _ { 1 }$\\
$2 x _ { 1 } - 3 x _ { 2 } + 2 x _ { 3 } = \lambda x _ { 2 }$\\
$- x _ { 1 } + 2 x _ { 2 } = \lambda x _ { 3 }$\\
has a non-trivial solution,\\
(1) Contains more than two elements.\\
(2) Is an empty set.\\
(3) Is a singleton.\\
(4) Contains two elements.

Paper Questions

Q61 Q62 Q63 Q64 Q65 Q66 Q67 Q68 Q69 Q70 Q71 Q72 Q73 Q74 Q75 Q76 Q77 Q78 Q79 Q80 Q81 Q82 Q83 Q84 Q85 Q86 Q87 Q88 Q89 Q90