Which of the following are correct in respect of the system of equations x+y+z=8, x-y+2 z=6 and 3 x-y+5 z=k ? 1. They have no solution. if k =15 . 2. They have infinitely many solutions, if k=20 . 3. They have unique solution, if k =25 Select the correct answer using the code given below:

Step-by-step solution

Here [ array ccc 1 & 1 & 1 1 & -1 & 2 3 & -1 & 5 array ] [ array l x y z array ]= [ array l 8 6 k array ] or A X=B . |A|=0( the system does not have a unique solution ) Now, ( Adj A)= [ array ccc -3 & -6 & 3 1 & 2 & -1 2 & 4 & -2 array ] and B= [ array c 8 6 k array ] For k=15,( Adj A) B= [ array c -24-36+15 8+12-15 16+24-30 array ]= [ array c -45 5 10 array ] 0 ( system is inconsistent i.e., it has no solution) For k=20,( Adj A) B= [ array c -24-36+60 8+12-20 16+24-40 array ]= [ array l 0 0 0 array ]=0 ( system ha