Class 12Mathematics3-4. Matrices and DeterminantsExpansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line
EasyIf $\left| \begin{array}{ccc} a & b & 0 \\ 0 & a & b \\ b & 0 & a \end{array} \right| = 0$,then
- A$a$ is one of the cube roots of unity
- B$b$ is one of the cube roots of unity
- C$\left( \frac{a}{b} \right)$ is one of the cube roots of unity
- D$\left( \frac{a}{b} \right)$ is one of the cube roots of $-1$
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Similar Questions
Evaluate the determinant: $\left|\begin{array}{cc}\sin \frac{11 \pi}{36} & \cos \frac{11 \pi}{36} \\\sin \frac{2 \pi}{9} & \cos \frac{2 \pi}{9}\end{array}\right|$.
Three points $(p + 1, 1)$,$(2p + 1, 3)$ and $(2p + 2, 2p)$ are collinear,if $p =$
Easy
View SolutionIf $\omega$ is a cube root of unity,then $\left| \begin{array}{ccc} x + 1 & \omega & \omega^2 \\ \omega & x + \omega^2 & 1 \\ \omega^2 & 1 & x + \omega \end{array} \right| = $
Easy
View SolutionIf $A = \begin{bmatrix} 0 & x & 16 \\ x & 5 & 7 \\ 0 & 9 & x \end{bmatrix}$ is a singular matrix,then the possible values of $x$ are:
The constant term of the polynomial $\left|\begin{array}{ccc}x+3 & x & x+2 \\ x & x+1 & x-1 \\ x+2 & 2x & 3x+1\end{array}\right|$ is
MediumKCET 2010
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