Class 12Mathematics3 and 4 .Determinants and MatricesRank of Matrices , Some special determinants, differentiation and integration of determinants
DifficultThe rank of $\left[\begin{array}{ccc}1 & -1 & 1 \\ 1 & 1 & -1 \\ -1 & 1 & 1\end{array}\right]$ is
- A$0$
- B$1$
- C$2$
- D$3$
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If $f(x) = \begin{vmatrix} x & x^2 & x^3 \\ 1 & 2x & 3x^2 \\ 0 & 2 & 6x \end{vmatrix}$,then the ratio $f^{\prime \prime}(x) : f^{\prime}(x) =$
DifficultAP EAMCET 2021
View SolutionWhat is the rank of the matrix $\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right]$?
Let $A = \begin{bmatrix} 1 & 0 & -1 & -3 \\ 0 & 1 & 1 & k-1 \\ 0 & 0 & k-1 & 1 \end{bmatrix}$ and $k \in R$. Then,the value of $k$,if it exists,for which the rank of $A$ is $2$,is
If $y = \sin(mx)$,then the value of $\left| \begin{array}{ccc} y & y_1 & y_2 \\ y_3 & y_4 & y_5 \\ y_6 & y_7 & y_8 \end{array} \right|$ (where subscripts of $y$ denote the order of derivative) is:
Difficult
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