Class 12Mathematics3 and 4 .Determinants and MatricesExpansion 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
If $A = \begin{bmatrix} 1 & 1 & a+1 \\ 1 & a+1 & 1 \\ a+1 & 1 & 1 \end{bmatrix}$ is not an invertible matrix,then the sum of all the values of $a$ is
If $a, b, c$ are positive and not all equal,then the value of the determinant $\left| \begin{array}{ccc} a & b & c \\ b & c & a \\ c & a & b \end{array} \right|$ is
MediumIIT 1982
View SolutionIf $\omega$ is a cube root of unity,then a root of the equation $\left| \begin{array}{ccc} x+1 & \omega & \omega^2 \\ \omega & x+\omega^2 & 1 \\ \omega^2 & 1 & x+\omega \end{array} \right| = 0$ is
Easy
View SolutionThe constant term in the expansion of $ \left|\begin{array}{ccc} 3x+1 & 2x-1 & x+2 \\ 5x-1 & 3x+2 & x+1 \\ 7x-2 & 3x+1 & 4x-1 \end{array}\right| $ is
DifficultKCET 2019
View SolutionIf $\left[\begin{array}{rrr}1 & -1 & x \\ 1 & x & 1 \\ x & -1 & 1\end{array}\right]$ has no inverse, then the real value of $x$ is
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