jee-main 2020 Q62

jee-main · India · session2_02sep_shift2 Matrices Linear System and Inverse Existence

Let $A = \left\{ X = ( x , y , z ) ^ { T } : P X = 0 \text{ and } x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 1 \right\}$ where $P = \left[ \begin{array} { c c c } 1 & 2 & 1 \\ - 2 & 3 & - 4 \\ 1 & 9 & - 1 \end{array} \right]$ then the set $A$
(1) Is a singleton.
(2) Is an empty set.
(3) Contains more than two elements
(4) Contains exactly two elements

Let $A = \left\{ X = ( x , y , z ) ^ { T } : P X = 0 \text{ and } x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 1 \right\}$ where $P = \left[ \begin{array} { c c c } 1 & 2 & 1 \\ - 2 & 3 & - 4 \\ 1 & 9 & - 1 \end{array} \right]$ then the set $A$\\
(1) Is a singleton.\\
(2) Is an empty set.\\
(3) Contains more than two elements\\
(4) Contains exactly two elements

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