The determinant $\,\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&2&3\\1&3&6\end{array}\,} \right|$ is not equal to
The determinant $\,\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&2&3\\1&3&6\end{array}\,} \right|$ is not equal to
- A
$\left| {\,\begin{array}{*{20}{c}}2&1&1\\2&2&3\\2&3&6\end{array}\,} \right|$
- B
$\left| {\,\begin{array}{*{20}{c}}2&1&1\\3&2&3\\4&3&6\end{array}\,} \right|$
- C
$\left| {\begin{array}{*{20}{c}}1&2&1\\1&5&3\\1&9&6\end{array}} \right|$
- D
$\left| {\,\begin{array}{*{20}{c}}3&1&1\\6&2&3\\{10}&3&6\end{array}} \right|\,$
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If the system of linear equations $2x + 2y + 3z = a$ ; $3x - y + 5z = b$ ; $x - 3y + 2z = c$ Where $a, b, c$ are non zero real numbers, has more than one solution, then
If the system of linear equations $2x + 2y + 3z = a$ ; $3x - y + 5z = b$ ; $x - 3y + 2z = c$ Where $a, b, c$ are non zero real numbers, has more than one solution, then
- [JEE MAIN 2019]
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If ${a^2} + {b^2} + {c^2} + ab + bc + ca \leq 0\,\forall a,\,b,\,c\, \in \,R$ , then the value of determinant $\left| {\begin{array}{*{20}{c}}
{{{(a + b + c)}^2}}&{{a^2} + {b^2}}&1 \\
1&{{{(b + c + 2)}^2}}&{{b^2} + {c^2}} \\
{{c^2} + {a^2}}&1&{{{(c + a + 2)}^2}}
\end{array}} \right|$
If ${a^2} + {b^2} + {c^2} + ab + bc + ca \leq 0\,\forall a,\,b,\,c\, \in \,R$ , then the value of determinant $\left| {\begin{array}{*{20}{c}}
{{{(a + b + c)}^2}}&{{a^2} + {b^2}}&1 \\
1&{{{(b + c + 2)}^2}}&{{b^2} + {c^2}} \\
{{c^2} + {a^2}}&1&{{{(c + a + 2)}^2}}
\end{array}} \right|$