Class 12Mathematics3-4. Matrices and DeterminantsExpansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line
EasyEvaluate the determinant: $\left|\begin{array}{cc}2 & 4 \\ -5 & -1\end{array}\right|$
- A$10$
- B$18$
- C$22$
- D$15$
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If matrix $A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$,then $|A|^{-1}$ is equal to
If $A=\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4\end{array}\right]$,then show that $|3 A|=27|A|$.
Easy
View SolutionFor $0 < \theta < \frac{\pi}{2}$,if $A = \begin{bmatrix} 1 & -\cos \theta & -1 \\ \cos \theta & 1 & -\cos \theta \\ 1 & \cos \theta & 1 \end{bmatrix}$,then which of the following is true regarding $\operatorname{det}(A)$?
If $f(x) = \begin{vmatrix} 1 & x & x+1 \\ 2x & x(x-1) & (x+1)x \\ 3x(x-1) & x(x-1)(x-2) & (x+1)x(x-1) \end{vmatrix}$, then $f(100)$ is equal to:
MediumWBJEE 2015
View SolutionIf $A = \begin{bmatrix} 5 & 5\alpha & \alpha \\ 0 & \alpha & 5\alpha \\ 0 & 0 & 5 \end{bmatrix}$ and $\operatorname{det}(A^2) = 25$, then $|\alpha| = $
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