Class 12Mathematics3 and 4 .Determinants and MatricesRank of Matrices , Some special determinants, differentiation and integration of determinants
EasyIn a matrix $A$,if all the sub-matrices of order $k$ are singular and there is at least one non-singular sub-matrix of order $r$ $(r < k)$,then the rank $(\rho)$ of the matrix $A$:
- Asatisfies $r \leq \rho < k$
- Bis equal to $r$
- Cis equal to $(k-1)$
- Dis equal to $(k+1)$
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Difficult
View SolutionThe determinant $\left| \begin{array}{ccc} ^x{C_1} & ^x{C_2} & ^x{C_3} \\ ^y{C_1} & ^y{C_2} & ^y{C_3} \\ ^z{C_1} & ^z{C_2} & ^z{C_3} \end{array} \right|$ equals:
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