Class 12Mathematics3-4. Matrices and DeterminantsRank of Matrices , Some special determinants, differentiation and integration of determinants
EasyIf there exists a $k^{\text{th}}$ order non-singular submatrix in a matrix $P$ of order $m \times n$,then the rank $(\rho)$ of $P$
- Asatisfies $k \leq \rho \leq m$
- Bsatisfies $k < \rho < n$
- Csatisfies $k \leq \rho \leq \min \{m, n\}$
- Dis equal to $k+1$
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Similar Questions
Which of the following matrices has rank $3$?
The rank of $A = \begin{bmatrix} 1 & x & x+1 \\ 2x & x^2-x & x^2+x \\ 3x(x-1) & x(x^2-3x+2) & x(x^2-1) \end{bmatrix}$ is:
DifficultTS EAMCET 2020
View SolutionIf the matrix $A=\left[\begin{array}{cccc}1 & 2 & 3 & 0 \\ 2 & 4 & 3 & 2 \\ 3 & 2 & 1 & 3 \\ 6 & 8 & 7 & \alpha\end{array}\right]$ is of rank $3$,then $\alpha$ equals to
DifficultTS EAMCET 2014
View Solution$A$ value of $b$ for which the rank of the matrix $A = \begin{bmatrix} 1 & 1 & -1 & 0 \\ 4 & 4 & -3 & 1 \\ b & 2 & 2 & 2 \\ 9 & 9 & b & 3 \end{bmatrix}$ is $3$,is
Let $f(x) = \left| \begin{array}{ccc} 1 + \sin^2 x & \cos^2 x & 4 \sin 2x \\ \sin^2 x & 1 + \cos^2 x & 4 \sin 2x \\ \sin^2 x & \cos^2 x & 1 + 4 \sin 2x \end{array} \right|$,then the maximum value of $f(x)$ is:
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