Tag: system of simultaneous equations
Questions Related to system of simultaneous equations
For the system of linear equations 2x + 3y + 5z = 9, 7x + 3y - 2z = 8 and 2x + 3y +$\lambda$z $=\mu$.Under what condition does the above system of equations have infinitely many solutions.
The system $2x+3y+z=5, 3x+y+5z=7, x+4y-2z=3$ has:
If AX = B where A is $3 \times 3$ and X and B are $3\times 1$ matrices then which of the following is correct?
The system of equations , $ ax+y+z = a-1 $ , $x+ay+z = a-1 $, $x+y+az = a-1 $has no solution, if a is
The three distinct straight lines $ax+by+c=0$;$bx+cy+a=0$ and $cx+ay+b=0$ are concurrent then
If $\omega$ is a cube root of unity and $x+ y + z = a, x + \omega y + \omega^2 z = b, x + \omega^2 y + \omega z = c$, then $x = $ ............
If $f(x) = ax^2 + bx + c, a, b, c \in R$ and equation $f(x)- x = 0$ has non-real roots $\alpha, \beta$. Let $\gamma, \delta$ be the roots of $f(f(x)) - x = 0$ ($\gamma, \delta$ are not equal to $\alpha, \beta$). Then $\begin{vmatrix} 2 & \alpha & \delta\ \beta & 0 & \alpha\ \gamma & \beta & 1\end{vmatrix} $ is
If $\displaystyle \omega$ is cube root of unity and $\displaystyle x + y + z = a$, $\displaystyle x + \omega y + \omega^{2} z = b$, $\displaystyle x + \omega^{2} y + \omega z = b$ then which of the following is not correct?
Consider the system of equations $x-2y+3z=-1,
-x+y-2z=k , x-3y+4z=1$
STATEMENT - 2 : The determinant $\begin{vmatrix}
1 & 3 & -1\
-1 & -2& k\
1& 4& 1
\end{vmatrix}$ $\neq 0$ for $k\neq 3$
The values of $\theta $ lying between $\theta =0$ and $\theta =\dfrac {\pi}{2}$ and satisfying the equation
$\begin{vmatrix}
1+\sin ^{2}\theta & \cos ^{2}\theta & 4\sin 6\theta \
\sin ^{2}\theta & 1+\cos ^{2}\theta & 4\sin 6\theta \
\sin ^{2}\theta & \cos ^{2}\theta & 1+4\sin 6\theta
\end{vmatrix}$
are given by