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
EasyThe area of a triangle whose vertices are $(1, -1)$,$(-1, 1)$,and $(-1, -1)$ is given by
- A$2$
- B$0.5$
- C$1$
- D$3$
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If $A = \begin{bmatrix} 2-k & 2 \\ 1 & 3-k \end{bmatrix}$ is a singular matrix,then the value of $5k - k^2$ is equal to
If $\left| \begin{array}{ccc} 6i & -3i & 1 \\ 4 & 3i & -1 \\ 20 & 3 & i \end{array} \right| = x + iy$,then $(x, y)$ is
Easy
View SolutionIf $\left| \begin{array}{ccc} a & b & c \\ b & c & a \\ c & a & b \end{array} \right| = k(a + b + c)(a^2 + b^2 + c^2 - bc - ca - ab)$,then $k =$
Medium
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 1986
View SolutionIf $\left| \begin{array}{ccc} 1 & 2 & 3 \\ 2 & x & 3 \\ 3 & 4 & 5 \end{array} \right| = 0$,then $x =$
Easy
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