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
DifficultThe value of the determinant $\left| \begin{array}{ccc} -1 & 1 & 1 \\ 1 & -1 & 1 \\ 1 & 1 & -1 \end{array} \right|$ is equal to
- A$-4$
- B$0$
- C$1$
- D$4$
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Similar Questions
Prove that $\left|\begin{array}{ccc}b+c & a & a \\ b & c+a & b \\ c & c & a+b\end{array}\right|=4abc$
Medium
View SolutionIf ${\Delta _1} = \left| {\begin{array}{*{20}{c}}1&0\\a&b\end{array}} \right|$ and ${\Delta _2} = \left| {\begin{array}{*{20}{c}}1&0\\c&d\end{array}} \right|$,then ${\Delta _2}{\Delta _1}$ is equal to
Easy
View SolutionThe determinant $\left| \begin{array}{ccc} a & b & a\alpha + b \\ b & c & b\alpha + c \\ a\alpha + b & b\alpha + c & 0 \end{array} \right| = 0$,if $a, b, c$ are in
MediumIIT 1987
View SolutionIf $A$,$B$ and $C$ are the angles of a triangle,then the value of the determinant $\left| \begin{array}{ccc} -1 + \cos B & \cos C + \cos B & \cos B \\ \cos C + \cos A & -1 + \cos A & \cos A \\ -1 + \cos B & -1 + \cos A & -1 \end{array} \right|$ is:
Let $A=\begin{bmatrix} 2 & 2+p & 2+p+q \\ 4 & 6+2p & 8+3p+2q \\ 6 & 12+3p & 20+6p+3q \end{bmatrix}$. If $\operatorname{det}(\operatorname{adj}(\operatorname{adj}(3A)))=2^m \cdot 3^n$,where $m, n \in N$,then $m+n$ is equal to:
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