Q67
Two matrices A and B are given below: \[ A = [ array*20c p& q \\ r& s array ] ;\, B = [ array*20c p^2 + q^2& pr + qs \\ pr + qs& r^2 + s^2 array ]\] If the rank of matrix A is N, then the rank of matrix B is
Two matrices A and B are given below:
{\text{A}} = \left[ {\begin{array}{*{20}{c}} {\text{p}}&{\text{q}} \\ {\text{r}}&{\text{s}} \end{array}} \right]{\text{;}}\,{\text{B}} = \left[ {\begin{array}{*{20}{c}} {{{\text{p}}^2} + {{\text{q}}^2}}&{{\text{pr}} + {\text{qs}}} \\ {{\text{pr}} + {\text{qs}}}&{{{\text{r}}^2} + {{\text{s}}^2}} \end{array}} \right]
If the rank of matrix A is N, then the rank of matrix B is
{\text{A}} = \left[ {\begin{array}{*{20}{c}} {\text{p}}&{\text{q}} \\ {\text{r}}&{\text{s}} \end{array}} \right]{\text{;}}\,{\text{B}} = \left[ {\begin{array}{*{20}{c}} {{{\text{p}}^2} + {{\text{q}}^2}}&{{\text{pr}} + {\text{qs}}} \\ {{\text{pr}} + {\text{qs}}}&{{{\text{r}}^2} + {{\text{s}}^2}} \end{array}} \right]
If the rank of matrix A is N, then the rank of matrix B is
A.
B.
N - 1
C.
N
AnswerD.
2N
Answer: Option C
Solution
Answer: Option C
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