A) 1 if \[a=6\]
B) 2 if \[a=1\]
C) 3 if \[a=2\]
D) 1 if\[a=4\]
Correct Answer: B
Solution :
[b] Let \[A=\left[ \begin{matrix} -1 & 2 & 5 \\ 2 & -4 & a-4 \\ 1 & -2 & a+1 \\ \end{matrix} \right]\tilde{\ }\left[ \begin{matrix} -1 & 2 & 5 \\ 0 & 0 & a+6 \\ 0 & 0 & a+6 \\ \end{matrix} \right]\] \[[{{R}_{2}}\to {{R}_{2}}+2{{R}_{1}},\,{{R}_{3}}\to {{R}_{3}}+{{R}_{1}}]\] Clearly rank of A is 1 if \[a=-6\] Also, for \[a=1,\] \[|A|=\left| \begin{matrix} -1 & 2 & 5 \\ 2 & -4 & -3 \\ 1 & -2 & 2 \\ \end{matrix} \right|=0\] and \[\left| \begin{matrix} 2 & 5 \\ -4 & -3 \\ \end{matrix} \right|=-6+20=14\ne 0\] \[\therefore \] rank of A is 2 if \[a=1\]
You need to login to perform this action.
You will be redirected in
3 sec
