| If the system of equations |
| x + y + z = 5 |
| x + 2y + 3z = 9 |
| \[x+3y+az=\beta \] |
| has infinitely many solutions, then p - a equals: |
A) 21
B) 8
C) 18
D) 5
Correct Answer: B
Solution :
| \[x+y-z=5\] |
| \[x+2y+3z=9.\] |
| \[x+3y+az=\beta \] |
| \[D=\left| \begin{matrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 0 \\ \end{matrix} \right|=0\] |
| \[\Rightarrow \] \[(2\alpha -9)+(3-\alpha )+(3-2)=0\] |
| \[\Rightarrow \] \[\alpha =5\] |
| Now, \[{{D}_{3}}=\left| \begin{matrix} 1 & 1 & 5 \\ 1 & 2 & 9 \\ 1 & 2 & \beta \\ \end{matrix} \right|=0\] |
| \[\Rightarrow \] \[2\beta -27+9\beta -5(3-2)=0\] |
| \[\Rightarrow \] \[\beta =13\] |
| \[\Rightarrow \] at \[\alpha =5,~\beta =13\]above 3 planes from common line. |
You need to login to perform this action.
You will be redirected in
3 sec
