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 $f(x) = \left| \begin{array}{ccc} 1 & 6+x & 36+x^2 \\ 0 & x-3 & 3x^2-27 \\ 0 & 2x-4 & 8x^2-32 \end{array} \right|$,then $\lim_{x \rightarrow 1} \frac{f(x)}{f(-x)} = $
Find the equation of the line joining $(3, 1)$ and $(9, 3)$ using determinants.
Easy
View SolutionIf the points with position vectors $60 \hat{i}+3 \hat{j}$,$40 \hat{i}-8 \hat{j}$,and $a \hat{i}-52 \hat{j}$ are collinear,then $a$ is equal to
DifficultTS EAMCET 2008
View Solution$l, m, n$ are the $p^{th}, q^{th}$ and $r^{th}$ terms of a $G$.$P$.,all positive,then $\left| \begin{array}{ccc} \log l & p & 1 \\ \log m & q & 1 \\ \log n & r & 1 \end{array} \right|$ equals
MediumAIEEE 2002
View SolutionThe solutions of $\operatorname{det}(A-\lambda I_2)=0$ are $4$ and $8$,where $A=\begin{bmatrix} 2 & 3 \\ x & y \end{bmatrix}$. Then:
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