Question

hello
determinants class 12 solve this problem

I will give brainlist for correct answer​

Answer 1

So we have the matrices having determinants,

$\mid D\mid=\left|\begin {array}{ccc}1&1&1\\3&3&1\\2&3&2\end {array}\right|=3-4+3=2\\\\\mid D_x\mid=\left|\begin {array}{ccc}6&1&1\\12&3&1\\14&3&2\end {array}\right|=18-10-6=2\\\\\mid D_y\mid=\left|\begin {array}{ccc}1&6&1\\3&12&1\\2&14&2\end {array}\right|=10-24+18=4\\\\\mid D_z\mid=\left|\begin {array}{ccc}1&1&6\\3&3&12\\2&3&14\end {array}\right|=6-18+18=6$

Now, by Cramer's Rule,

$x=\dfrac{|D_x|}{|D|}=\dfrac {2}{2}=\mathbf{1}\\\\y=\dfrac{|D_y|}{|D|}=\dfrac {4}{2}=\mathbf{2}\\\\z=\dfrac{|D_z|}{|D|}=\dfrac {6}{2}=\mathbf{3}$