If $2x + 3y - 5z = 7, \,x + y + z = 6$, $3x - 4y + 2z = 1,$ then $x =$
$\left| {\,\begin{array}{*{20}{c}}2&{ - 5}&7\\1&1&6\\3&2&1\end{array}\,} \right| \div \left| {\,\begin{array}{*{20}{c}}7&3&{ - 5}\\6&1&1\\1&{ - 4}&2\end{array}\,} \right|$
$\left| {\,\begin{array}{*{20}{c}}{ - 7}&3&{ - 5}\\{ - 6}&1&1\\{ - 1}&{ - 4}&2\end{array}\,} \right| \div \left| {\,\begin{array}{*{20}{c}}2&3&{ - 5}\\1&1&1\\3&{ - 4}&2\end{array}\,} \right|$
$\left| {\,\begin{array}{*{20}{c}}7&3&{ - 5}\\6&1&1\\1&{ - 4}&2\end{array}\,} \right| \div \left| {\,\begin{array}{*{20}{c}}2&3&{ - 5}\\1&1&1\\3&{ - 4}&2\end{array}\,} \right|$
None of these
For how many diff erent values of $a$ does the following system have at least two distinct solutions?
$a x+y=0$
$x+(a+10) y=0$
If the system of equations
$2 x+y-z=5$
$2 x-5 y+\lambda z=\mu$
$x+2 y-5 z=7$
has infinitely many solutions, then $(\lambda+\mu)^2+(\lambda-\mu)^2$ is equal to
The system of linear equations $x + y + z = 2$, $2x + y - z = 3,$ $3x + 2y + kz = 4$has a unique solution if
The roots of the equation $\left| {\,\begin{array}{*{20}{c}}x&0&8\\4&1&3\\2&0&x\end{array}\,} \right| = 0$ are equal to
If $'a'$ is non real complex number for which system of equations $ax -a^2y + a^3z$ = $0$ , $-a^2x + a^3y + az$ = $0$ and $a^3x + ay -a^2z$ = $0$ has non trivial solutions, then $|a|$ is