Embibe Experts Solutions for Chapter: Determinants, Exercise 1: Haryana Board-2018

Find the area of triangle whose vertices are $(-1,1,2), (1,2,3), (2,5,-1)$

The value of $x$ for which $\left|\begin{array}{ll}3& x\\ x& 1\end{array}\right|=\left|\begin{array}{ll}3& 2\\ 4& 1\end{array}\right|$ is :

If $A=\left[\begin{array}{ll}1& 2\\ 4& 2\end{array}\right]$ then show that $\left|2A\right|=4\left|A\right|$.

Solve the system of linear equations by matrix method

$\mathrm{x}-\mathrm{y}+\mathrm{z}=4$

$2\mathrm{x}+\mathrm{y}-3\mathrm{z}=0$

$x+y+z=2$

If $\left|\begin{array}{ll}2& 4\\ 5& 1\end{array}\right|=\left|\begin{array}{cc}2x& 4\\ 6& x\end{array}\right|$, then the value of $x$ is :

Prove that $\left|\begin{array}{ccc}y+k& y& y\\ y& y+k& y\\ y& y& y+k\end{array}\right|=k^2\left(3y+k\right)$

The vertices of a triangle $\mathrm{ABC}$ are given by position vector $A(\hat{i}+\hat{j}+2\hat{k}),B(2\hat{i}+3\hat{j}+5\hat{k})$ and $C(\hat{i}+5\hat{j}+5\hat{k})$. Find its area.

Solve the system of linear equations by matrix method 

$2x+3y+3z=5$

$x-2y+z=-4$

$3x-y-2z=3$