If 2x + 3y - 5z = 7, ,x + y + z = 6 , 3x

Hindi

3 and 4 .Determinants and Matrices

medium

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

Solution

$x = \frac{{{D_x}}}{D} = \left| {\,\begin{array}{*{20}{c}}7&{\,\,3}&{ – 5}\\6&{\,\,1}&{\,\,1}\\1&{ – 4}&{\,\,2}\end{array}\,} \right|\, \div \left| {\,\begin{array}{*{20}{c}}2&{\,\,3}&{ – 5}\\1&{\,\,1}&{\,\,1}\\3&{ – 4}&{\,\,2}\end{array}\,} \right|$.

Standard 12

Mathematics

For which of the following ordered pairs $(\mu, \delta)$ the system of linear equations $x+2 y+3 z=1$ ; $3 x+4 y+5 z=\mu$ ; $4 x+4 y+4 z=\delta$ is inconsistent?

hard

(JEE MAIN-2020)

Evaluate $\Delta=\left|\begin{array}{ccc}0 & \sin \alpha & -\cos \alpha \\ -\sin \alpha & 0 & \sin \beta \\ \cos \alpha & -\sin \beta & 0\end{array}\right|$

easy

If $\omega $ be a complex cube root of unity, then $\left| {\,\begin{array}{*{20}{c}}1&\omega &{ – {\omega ^2}/2}\\1&1&1\\1&{ – 1}&0\end{array}\,} \right| = $

medium

Find equation of line joining $(3,1)$ and $(9,3)$ using determinants

easy

Set of equations $a + b – 2c = 0,$ $2a – 3b + c = 0$ and $a – 5b + 4c = \alpha $ is consistent for $\alpha$ equal to

medium