If the system of linear equation $x - 4y + 7z = g,\,3y - 5z = h, \,-\,2x + 5y - 9z = k$ is
consistent, then
If the system of linear equation $x - 4y + 7z = g,\,3y - 5z = h, \,-\,2x + 5y - 9z = k$ is
consistent, then
- [JEE MAIN 2019]
- A
$g+h+k=0$
- B
$2g+h+k=0$
- C
$g+h+2k=0$
- D
$g+2h+k=0$
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The value of the determinant $\left| {\begin{array}{*{20}{c}}{{a^2}}&a&1\\{\cos \,(nx)}&{\cos \,(n\, + \,1)\,x}&{\cos \,(n\, + \,2)\,x}\\{\sin \,(nx)}&{\sin \,(n\, + \,1)\,x}&{\sin \,(n\, + \,2)\,x}\end{array}} \right|$ is independent of :
The values of $a$ and $b$, for which the system of equations $2 x+3 y+6 z=8$ ; $x+2 y+a z=5$ ; $3 x+5 y+9 z=b$ has no solution, are:
The values of $a$ and $b$, for which the system of equations $2 x+3 y+6 z=8$ ; $x+2 y+a z=5$ ; $3 x+5 y+9 z=b$ has no solution, are:
- [JEE MAIN 2021]
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$\left| {\,\begin{array}{*{20}{c}}{a - b}&{b - c}&{c - a}\\{x - y}&{y - z}&{z - x}\\{p - q}&{q - r}&{r - p}\end{array}\,} \right| = $
Let $\left| {\,\begin{array}{*{20}{c}}{6i}&{ - 3i}&1\\4&{3i}&{ - 1}\\{20}&3&i\end{array}\,} \right| = x + iy$, then
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- [IIT 1998]
Let $S$ be the set of all real values of $k$ for which the system oflinear equations $x +y + z = 2$ ; $2x +y - z = 3$ ; $3x + 2y + kz = 4$ has a unique solution. Then $S$ is
Let $S$ be the set of all real values of $k$ for which the system oflinear equations $x +y + z = 2$ ; $2x +y - z = 3$ ; $3x + 2y + kz = 4$ has a unique solution. Then $S$ is
- [JEE MAIN 2018]