A) 1
B) -1
C) 0
D) pqr
Correct Answer: C
Solution :
Let first term = A and common difference = D \[\therefore a=A+(p-1)D\], \[b=A+(q-1)D\], \[c=A+(r-1)D\] \[\left| \begin{matrix} \,a\,\,\, & p\,\,\, & 1\, \\ \,b\,\,\, & q\,\,\, & 1 \\ \,c\,\,\, & r\,\,\, & 1 \\ \end{matrix} \right|=\left| \begin{matrix} \,A+(p-1)D\,\,\, & p\,\,\, & 1\, \\ A+(q-1)D\,\,\, & q\,\,\, & 1 \\ A+(r-1)D\,\,\, & r\,\,\, & 1 \\ \end{matrix} \right|\] Operate \[{{C}_{1}}\to {{C}_{1}}-D{{C}_{2}}+D{{C}_{3}}\] \[=\,\left| \begin{matrix} \,A\,\, & p\,\, & 1\, \\ \,A\,\, & q\,\, & 1 \\ \,A\,\, & r\,\, & 1 \\ \end{matrix} \right|=A\left| \begin{matrix} \,\,1 & \,\,p & \,\,1\, \\ \,1 & q & 1 \\ \,1 & r & 1 \\ \end{matrix} \right|=0\].You need to login to perform this action.
You will be redirected in
3 sec