The system of linear equation x + y + z = 2, | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

By applying Crammer's Rule

$D = \left| {\begin{array}{*{20}{c}}
1&1&1\
2&3&2\
2&3&{{a^2} - 1}
\end{array}} ight

Vedclass · Accepted Answer

inconsistent when $\left| a \right| = \sqrt 3 $

Vedclass · Answer

By applying Crammer's Rule

$D = \left| {\begin{array}{*{20}{c}}
1&1&1\
2&3&2\
2&3&{{a^2} - 1}
\end{array}} ight|$

$ = 3\left( {{a^2} - 1} ight) - 6 - 2\left( {{a^2} - 1} ight) + 4$

$ = {a^2} - 1 - 2 = {a^2} - 3$

If $\left| a ight| 
e  \pm \sqrt 3  \Rightarrow $system has unique solution

If $\left| a ight| = \sqrt 3 \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left. \begin{array}{l}
x + y + z = 1\
2x + 3y + 2z = 1\
2x + 3y + 2z =  \pm \sqrt 3  + 1
\end{array} ight\}$

Hence system is inconsistent for $\left| a ight| = \sqrt 3 $

The system of linear equation $x + y + z = 2, 2x + 3y + 2z = 5$, $2x + 3y + (a^2 -1)\,z = a + 1$ then

Similar Questions

The roots of the equation $\left| {\,\begin{array}{*{20}{c}}{x - 1}&1&1\\1&{x - 1}&1\\1&1&{x - 1}\end{array}\,} \right| = 0$ are

If $\left| {\begin{array}{*{20}{c}}{x - 4}&{2x}&{2x}\\{2x}&{x - 4}&{2x}\\{2x}&{2x}&{x - 4}\end{array}} \right| = \left( {A + Bx} \right){\left( {x - A} \right)^2},$ then the ordered pair $\left( {A,B} \right) = $. . . . .

Evaluate $\left|\begin{array}{cc}x & x+1 \\ x-1 & x\end{array}\right|$

Let $ \alpha _1, \alpha _2$ are two values of $\alpha $ for which the system $2 \alpha x + y = 5, x - 6y = \alpha $ and $x + y = 2$ is consistent, then $ |2(\alpha _1 + \alpha _2)| $ is -

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